  This contribution derives the exact asymptotic behaviour of the supremum of
alpha(t)-locally stationary Gaussian random fields over a finite hypercube. We
present two applications of our result; the first one deals with extremes of
ggregate multifractional Brownian motions, whereas the second application
establishes the exact asymptotics of the supremum of chi-processes generated by
multifractional Brownian motions.
