The Taylor expansion of the generalized spin-down equation = − f(v), derives into the multipolar equation = −gv 5 – rv 3 − sv), which is used here to study pulsar evolution. The coefficients g, r and s can be physically associated to gravitational radiation, magnetic dipolar radiation and particle aceleration. The multipolar expansion with constant coefficients cannot describe the P Ṗ diagram in a consistent manner and therefore it is unlikely a generalized equation of the form = −f(v;t) can be used to describe pulsar evolution. A more general form, = − f(v; t) can be investigated giving to the coefficients g, r and s time dependence. We consider some explicit functional forms for g(t), r(t) and s(t) which are consistent with observational and theoretical constraints.