I have a least three male relatives born between 1800 and 1810 that I cannot trace back further.
How should I continue my research?
( they all seem to be USA born Kentucky, Tennessee)
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Another strategy: Look at the census records which do list family members' names. Often families travelled to new locations in groups. It may be that the parents of one of these male relatives is living nearby or with a family member.
Ex: Stephen Brumley was born in the 18th century. His wife's father moved from Georgia to Alabama with them and is found on a later census living nearby. This helped me to go back one more generation and to make an educated guess as to the names of the family members on the 1790 census.
Another method to research early 1800's records is to research historical books and journals on the particular counties in the particular States.
The LDS have a vast online library.