  Different types of nonstandard homology groups based on the various
subcomplexes of differential forms are considered as a continuation of the
recent authors works. Some of them reflect interesting properties of dynamical
systems on the compact manifolds. In order to study them a Special Perturbation
Theory in the form of Spectral Sequences is developed. In some cases a
convenient fermionic formalism of dealing with differential forms is used
originated from the work of Witten in the Morse Theory (1982)and the authors
work where some nonstandard analog of Morse Inequalities for vector fields was
found (1986).
