  We present a new method for the momentum expansion of Feynman integrals with
arbitrary masses and any number of loops and external momenta. By using the
parametric representation we derive a generating function for the coefficients
of the small momentum expansion of an arbitrary diagram. The method is
applicable for the expansion w.r.t. all or a subset of external momenta. The
coefficients of the expansion are obtained by applying a differential operator
to a given integral with shifted value of the space-time dimension $d$ and the
expansion momenta set equal to zero. Integrals with changed $d$ are evaluated
by using the generalized recurrence relations proposed in \cite{OVT1}. We show
how the method works for one- and two-loop integrals. It is also illustrated
that our method is simpler and more efficient than others.
