Higher order two step mechanisms in nucleon antinucleon annihilation and the OZI rule

We evaluate three meson doorway mechanisms for nucleon-antinucleon annihila tion at rest for the first time. Detailed results are presented for the fin al state phi pi(0) originating from the S-3(1) initial state and for the ph i rho channel originating from S-1(0). The results presented also include t he improved contributions from two meson doorway states and from the tree d iagrams. For all the channels considered a consistent explanation of large and small OZI violations emerges.