  The hypothesis about possible existence of new class of particles able to
travel faster then light as a source of dark matter, recently formulated by L.
Gonzalez-Mesters, is analyzed. To this end the general geometrical model for
several kinds of matter with different Lorentziann structures coexisting on the
same manifold is introduced and the local energy density in cosmological
reference frame is calculated in two particular cases. It is shown that the
local energy density is positive in both considered cases and hence such models
really may describe cosmological dark matter. Nevertheless, some problems may
appear during the construction of the cosmological models or the models of the
compact objects. Moreover, the simplest generalization of the model lead to
some variants of vector-tensor theory of gravitation with preferable reference
frame which contradict to observations.
