In view is the “in those days, and also afterwards” portion of the Bible’s Genesis ch. 6 text. Of course, delving into the minutia of this text would take us far and beyond the confines of one article thus, let us quote the relevant portion and focus on the incursion issue.
This is Genesis 6:1-5 from the NASB:
Now it came about, when men began to multiply on the face of the land, and daughters were born to them, that the sons of God saw that the daughters of men were beautiful; and they took wives for themselves, whomever they chose.
Then the LORD said, "My Spirit shall not strive with man forever, because he also is flesh; nevertheless his days shall be one hundred and twenty years."
The Nephilim were on the earth in those days, and also afterward, when the sons of God came in to the daughters of men, and they bore children to them. Those were the mighty men who were of old, men of renown.
Then the LORD saw that the wickedness of man was great on the earth, and that every intent of the thoughts of his heart was only evil continually.
The aforementioned minutia gets into who are the sons of God, the daughters of men, the Nephilim, the mighty men of old renown, etc. For our purposes we will assert that the sons of God are divine or heavenly beings; some term them “angels” but this seems restrictive; for example, keep in mind that satan is not a fallen angel but a fallen cherub they most certainly are not humans and may very well just have been the category of being known as angels (sorry for the complication but it is meant to elucidate some fine points; keeping in mind that in Job 1:6 and 2:1 the sons of God appear before YHVH along with satan and cherubim are not a kind of angel; cherubs, angels, seraphim, etc. are different categories of being). The daughters of men are human women. The Nephilim is another name (an aka) for their offspring; the mighty men of old renown.
A fellow assertion is that the great deluge, the worldwide flood was to deal with the actions not of the sons of God but of the Nephilim/mighty men of old renown. The reasoning here (much of which is borrowed from extra-biblical texts aka commentaries, histories, etc.) is that they were giants who first consumed humanity’s resources, then consumed humans and finally each other—big appetites to fuel big bodies.
It is, indeed, specified that “My Spirit shall not strive with man forever” and that “the wickedness of man was great…evil continually” but on this view this is not problematic as the Nephilim are, after all, referred to as “men” as in “mighty men who were of old, men of renown.”
You see how the debates about these various issues can be cumbersome—important and yet, outside the context of this article.
So, if the flood was due to the Nephilim’s actions, then how is it that they were “on the earth in those days” but “also afterward”; were they not gotten rid of via drowning in the flood? In fact, whether the flood was due to their actions or those of humanity is irrelevant, regarding their deaths, as either way; they, as a whole, drowned to death. But the follow up question is when is “afterward”; is it after the flood or after the described event which is when they actually were birthed; the event took place in the days of Jared whilst the flood took place in the days of Noah, “Jared lived one hundred and sixty-two years, and became the father of Enoch” (Genesis 5:18).
There are basically two views with regards to the specific issue of “and also afterwards”:
1) There was one incursion (as it has been termed) by the sons of God.
2) There were multiple incursions by the sons of God.
However, this is no entirely accurate. Yes, the discussions on this specific point generally are termed one incursion or multiple incursions? Yet, view 1) consider that there were more than one incursion but that however many there were all took place pre-flood. Multiple implies one or more pre-flood and another of many more post-flood.
Thus, let us term the two basic views as Pre-Flood Incursionism and Pre & Post-Flood Incursionism both, generally, hold that the flood was due to the Nephilim and both ask of each other how it is that the flood did away with them and yet, they reappeared.
Pre-flood incursionists assert that while Noah himself was “perfect in his generation” his sons and daughters-in-law were not and so they carried the Nephilim genetic material into the ark with them and thus, ended up birthing (diluted) hybrids post-flood. Thus, the post-flood return of giants was not due to a post-flood incursion of sons of God but due to the expression of Nephilim genes.
The issue is that perfect is the same term used for the physical unblemished perfection (physical but not genetic; for details on this point see Was Noah genetically “perfect in his generation”?) of the animals to be sacrificed and so this leads to the view that he was not tainted by Nephilim genes.
Multiple incursionists assert that, as the term multiple incursion implies, after the flood the sons of God did it again (one more or many more times).
Pre-flood incursionists and pre & post-flood incursionists ask each other how the other’s position makes any sense. After all pre-flood incursionism has the Nephilim getting one over on YHVH, as it were, by making it through the flood via genetics. And the pre & post-flood incursionism has the Nephilim getting one over on YHVH, as it were, by making it through by simply doing it again.
In other words; they both have some 'splainin to do. That is to say that the texts must be elucidated as neither side can trump the other via taunts.
Let us take a step back to note that, with some Hebrew words placed into the English translation, the Nephilim portion of the text reads, “Those were the gibbowr who were of old, men of renown.” Gibbowr or Gibor is Strong’s #H1368 and does, indeed as the English translation denotes, 1) strong, mighty (adj) 2) strong man, brave man, mighty man (n m). It is an intensive from of the primitive root gabar (Strong’s #H1396): 1) to prevail, have strength, be strong, be powerful, be mighty, be great, etc.
Genesis 10 notes that Noah’s son Ham fathered Cush and that, in turn:
Cush became the father of Nimrod; he became a mighty one on the earth. He was a mighty hunter before the LORD; therefore it is said, “Like Nimrod a mighty hunter before the LORD.”
Two things to note; became is began to be and what Nimrod became/began to be is a mighty one which in Hebrew is gibbowr. So that he was a mighty hunter, was a gibbowr tsayid. It may be of interest to note that term/name Nimrod (Strong’s #H5248 Nimrowd) means “rebellion” or “the valiant.” Keep in mind that Nimrod spearheaded (pun intended; get it, hunter, spear…okay, no more punishment, even though it was very punny) the building of the Tower of Babel.
Clearly, in and of itself the term gibbowr/gibor denotes nothing more than might as in Deuteronomy 10:17 which states:
For the LORD your God is the God of gods and the Lord of lords, the great, the mighty [gibbowr], and the awesome God who does not show partiality nor take a bribe.
Thus, it is also used of anyone or anything that is mighty: lions (Proverbs 30:30), soldiers (Jeremiah 51:30), leaders in general (Daniel 11:3), the aforementioned hunter(s), etc. (and even comic book characters).
Due to the issues relating to the Nephilim as mighty/gibbowr men of old renown we get the concept of the Giborim—a “race” of giants. Yet, context determines meaning and the context is that these particularly gibbowrim, the Nephilim, were the sons of God (as defined above) and were of old which refers to very, very ancient times (old here being 'owlam Strong’s H5769).
Let us end here by providing some food for thought: the gibbowr Nimrod was directly related to Noah. Assuming (and some would think this to be quite the assumption) that his being a gibbowr refers to him not only being generically mighty but genetically mighty (as in giant) then how did he become one—via Noah’s wife’s, his son’s or his daughter-in-law’s genes?