  We propose to use diatomic molecular ions to search for strongly enhanced
effects of variation of fundamental constants. The relative enhancement occurs
in transitions between nearly degenerate levels of different nature. Since the
trapping techniques for molecular ions have already been developed, the
molecules HBr$^+$, HI$^+$, Br$^+_2$, I$^+_2$, IBr$^+$, ICl$^+$, and IF$^+$ are
very promising candidates for such future studies.
