  We present a new method to solve in a semianalytical way the
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in
the x-space. The method allows to construct an evolution operator expressed in
form of a rapidly convergent series of matrices, depending only on the
splitting functions. This operator, acting on a generic initial distribution,
provides a very accurate solution in a short computer time (only a few
hundredth of second). As an example, we apply the method, useful to solve a
wide class of systems of integrodifferential equations, to the polarized parton
distributions.
