  Zaharopol proved the following result: let $T,S:L^1(X,{\cf},\m)\to
L^1(X,{\cf},\m)$ be two positive contractions such that $T\leq S$. If
$\|S-T\|<1$ then $\|S^n-T^n\|<1$ for all $n\in\bn$. In the present paper we
generalize this result to multi-parameter contractions acting on $L^1$. As an
application of that result we prove a generalization of the "zero-two" law.
