Summary: Following an idea of D. Ornstein and L. Sucheston [Ann. Math. Stat. 41, 1631–1639 (1970; Zbl 0284.60068)], S. R. Foguel [Isr. J. Math. 10, 275–280 (1971; Zbl 0229.60056)] proved the so-called uniform “zero-two” law: let \(T:L^1(X,\mathcal{F},\mu) \to L^1(X,\mathcal{F},\mu)\) be a positive contraction. If for some \(m\in\mathbb N\cup\{0\}\) one has \(\| T^{m+1}-T^m\|<2\), then \[ \lim_{n\to\infty}\| T^{n+1}-T^n\|=0. \] There are many papers devoted to generalizations of this law. In the present paper, we provide a multi-parametric generalization of the uniform zero-two law for \(L^1\)-contractions.