It could be the refrigerator, freezer, a/c, etc. that pulls down on the circuit when they start as steve suggested.
It more likely may be a bad connection somewhere and possible on a neutral. Check all connections and under any wire nuts after shutting off the breakers and testing all wire with a meter for electricity(you can get electricity from another source if there is a short, etc). I suggest having an electrician doing this as electricity can kill. Good luck.