I am an Old Earth Creationist with the Day-Age Creationism variant. Old Earth, Day-Age Creationists hold that the six days that are reffered in Genesis are not ordinary 24-hour days, but insted the hebrew word for "day" (yom) can be interperate in this context to mean a long period of time (thousands or millions of years) rather than a 24-hour day. The Genesis account is interpreted as an account of a progressive creation, summary of life's evolutionary history.
To get into the grits and gravy on the core of my argument is that "day" is not literaly 24 hours but rather a long length of time. It has been noted that God is not bound by time (As referenced in Psalms 90:4, and other books) so the term "day" can be very arbitrary. Also the word day has multiple meanings in Hebrew. The most correct definition is "Time, period (general)". If we also look more into the Bible,
examples of yom as a long period of time include Genesis 2:4, Genesis 30:14, Joshua 24:7, Proverbs 25:13, Isaiah 4:2, Zechariah 14:8 and references to "the day of the Lord.". Also the term "day" in Genesis is used before the sun and moon were created or appeared (Gen. 1:5, 14-15.) and thus "day" does not refer to an Earthly day because such a day does not yet exist. Also the abstract use of "day" as an indefinite period of time is found in other mythological and religious writings of the Middle East to deote the passage of cosmic benchmarks in addition to referring to earthly time marked by the sun or the moon. Moveing on, Early Hebrews were very scant in words referring to periods of time. Since there was no word in early Hebrew with the meaning "period" and "season". Therefore if the author ment long creation days, he would have used the word "yom". There are other passages such as Daniel 8:14-26 that use "evening and morning" and yet applies to long periods of time. Also, Genesis 2:4 uses the word "yom" to refer to the entire creation account, which is obviously not 24 hours long in total. Thus, the word "yom" could have more abstract meaning.