On vanishing two loop cosmological constants in nonsupersymmetric strings

It has recently been suggested that in certain special nonsupersymmetric ty pe II string compactifications, at least the first two perturbative contrib utions to the cosmological constant Lambda vanish. Support for perturbative vanishing beyond 1-loop (as well as evidence for the absence of some nonpe rturbative contributions) has come from duality arguments. There was also a direct 2-loop computation which was incomplete; in this note we explain th e deficiency of the previous 2-loop calculation and discuss the complete 2- loop computation in two different models. The corrected analysis yields a v anishing 2-loop contribution to Lambda in these models.