Cancellation of leading divergences in multiloop closed superstring amplitudes

We discuss the general problem of divergences and the particularly important 'tadpole' configuration for multiloop amplitudes in the closed superstring - or heterotic string - covariant theory, with any number of external legs. We show that, due to a factor coming from the supermoduli, the tachyon divergence in the tadpole is cancelled in each spin structure contribution separately. (orig.)