Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $in$ (0, 1), -y"(t) = g(t, x(t)), t $in$ (0, 1), x(0) = y(0) = 0, x(1) = ${alpha}x(eta)$, y(1) = ${alpha}y(eta)$, are obtained. The nonlinearities f, g : (0,1) $ imes$ (0, $infty$ ) $ ightarrow$ (0, $infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $eta$, $alpha$, satisfy ${eta};{in};$ (0,1), 0 < $alpha$ < $1/{eta}$. An example is provided to illustrate the results.