  We have considered the Pauli-Zeldovich mechanism for the cancellation of the
ultraviolet divergences in vacuum energy. This mechanism arises because bosons
and fermions give contributions of the opposite signs. In contrast with the
preceding papers devoted to this topic wherein mainly free fields were studied,
here we have taken their interactions into account to the lowest order of
perturbation theory. We have constructed some simple toy models having
particles with spin 0 and spin 1/2, where masses of the particles are equal
while the interactions can be quite non-trivial.
