  We generalize to the eleven-dimensional superparticle Berkovits' prescription
for loop computations in the pure spinor approach to covariant quantization of
the superstring. Using these ten- and eleven-dimensional results, we compute
covariantly the following one-loop amplitudes: C\wedge X_8 in M-theory; B\wedge
X_8 in type II string theory and F^4 in type I. We also verify the consistency
of the formalism in eleven dimensions by recovering the correct classical
action from tree-level amplitudes. As the superparticle is only a first
approximation to the supermembrane, we comment on the possibility of extending
this construction to the latter. Finally, we elaborate on the relationship
between the present BRST language and the spinorial cohomology approach to
corrections of the effective action.
