  When two particles collide near a black hole, the energy in their center of
mass frame can, under certain conditions, grow unbounded. This is the
Banados-Silk-West effect. We show that this effect retains its validity even if
some force acts on a particle, provided some reasonable and weak restrictions
are imposed on this force. In the present work we discuss the case of
nonextremal horizons. The result under discussion is similar to that for
extremal horizons considered in our previous work.
