Using linearized superfields, R-4 terms in the Type II superstring eff
ective action compactified on T-2 are constructed as integrals in N =
2 D = 8 superspace. The structure of these super space integrals allow
s a simple proof of the R-4 non-renormalization theorems which were fi
rst conjectured by Green and Gutperle. (C) 1998 Elsevier Science B.V.