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Intervals of the parameter $\lambda$ are determined for which there exist positive solutions for the system of nonlinear differential equations, $u^{(n)} + \lambda a(t) f(v) = 0, \ v^{(n)} +\lambda b(t) g(u) = 0, $ for $0 < t <1$, and satisfying three-point nonlocal boundary conditions, $u(0) = 0, u'(0) = 0, \ldots, u^{(n-2)}(0) = 0, \ u(1)=\alpha u(\eta), v(0) = 0, v'(0) = 0, \ldots, v^{(n-2)}(0) = 0, \ v(1)=\alpha v(\eta)$. A Guo-Krasnosel'skii fixed point theorem is applied.