The presence of a far off-resonant intermediate level in a degenerate
three-level two-photon laser model manifests through a steady pump-dep
endent and a dynamic frequency shift on the laser equations. The stead
y shift strongly affects the pump threshold necessary for emission, pr
eventing it in certain cases. The dynamic shift makes the frequency pu
lling/pushing to be intensity-dependent and substantially modify the d
omains of existence and stability of the lasing solution permitting st
able operation for large cavity losses in certain cases.