  An exact renormalization equation (ERGE) accounting for an anisotropic
scaling is derived. The critical and tricritical Lifshitz points are then
studied at leading order of the derivative expansion which is shown to involve
two differential equations. The resulting estimates of the Lifshitz critical
exponents compare well with the $O(\epsilon ^{2}) $ calculations. In the case
of the Lifshitz tricritical point, it is shown that a marginally relevant
coupling defies the perturbative approach since it actually makes the fixed
point referred to in the previous perturbative calculations $O(\epsilon) $
finally unstable.
