All lights dim and blower slows down intermittently on a 2000 Oldsmobile Intrigue?

[Tim H]

I notice at night that while driving my head lights and all my dash lights will dim, along with my fan for the ventilation slowing down, all intermittently. It has become a distraction and I am worried that the lights will go out while I am driving on some back road. What could be causing this problem? I have replaced the battery and posts from the cables and the problem is still occuring.