  We present some exact results on the behavior of Branching and Annihilating
Random Walks, both in the Directed Percolation and Parity Conserving
universality classes. Contrary to usual perturbation theory, we perform an
expansion in the branching rate around the non trivial Pure Annihilation model,
whose correlation and response function we compute exactly. With this, the
non-universal threshold value for having a phase transition in the simplest
system belonging to the Directed Percolation universality class is found to
coincide with previous Non Perturbative Renormalization Group approximate
results. We also show that the Parity Conserving universality class has an
unexpected RG fixed point structure, with a PA fixed point which is unstable in
all dimensions of physical interest.
