  We consider multidimensional cosmological models with a generalized
space-time manifold M = R x M_1 ...x M_n, composed from a finite number of
factor spaces M_i, i=1,..n. While usually each factor space M_i is considered
to be some Riemannian space of integer dimension d_i, here it is, more
generally, a fractal space, the dimension of which is a smooth function d_i(t)
of time. Hence, besides the scale factor exponents ln a_i and their
derivatives, we consider also the dimensions d_i of the factor spaces as
classical dynamical variables. The classical equation of motions and the
corresponding Wheeler-de Witt equation are set up generally, and the
qualitative behaviour of the system is discussed for some specific model with 2
factor spaces.
