Recent research points to cross-generational damage from exposures

The first is a new study shows that children who were born within 10 years of both parents surviving the 1945 atomic bombing of Hiroshima have a higher rate of developing leukemia than children who only had one parent who was a survivor within 10 years of the blast.

The finding was unveiled in Nagasaki on June 3 at a conference on post-atomic bombing disorders. The Asahi Shimbun

Cross-generational damage can come from DNA damage OR, according to another theory, from material which is not a direct part of the DNA, but can still influence it. See this from the Spokesman-Review: Women with ovarian disease may have inherited it from great grandmothers who were exposed to toxic chemicals decades ago, according to a study by Washington State University researchers. (This may be the case for radiation exposure as well)

Japanese researchers are using the work to look into whether the descendents of atomic bomb survivors may be more susceptible to cancer and other diseases because of epigenetic changes inherited from their ancestors.