  We analyze the reduction to four dimensions of the R^4 terms which are part
of the ten-dimensional string effective actions, both at tree level and one
loop. We show that there are two independent combinations of R^4 present, at
one loop, in the type IIA four dimensional effective action, which means they
both have their origin in M-theory. The d=4 heterotic effective action also has
such terms. This contradicts the common belief thathere is only one R^4 term in
four-dimensional supergravity theories, given by the square of the Bel-Robinson
tensor. In pure N=1 supergravity this new R^4 combination cannot be directly
supersymmetrized, but we show that, when coupled to a scalar chiral multiplet
(violating the U(1) $R$-symmetry), it emerges in the action after elimination
of the auxiliary fields.
