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

(0, 1), -y"(t) = g(t, x(t)), t

(0, 1), x(0) = y(0) = 0, x(1) =

, y(1) =

, are obtained. The nonlinearities f, g : (0,1)

(0,

)

(0,

) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters

,

, satisfy

(0,1), 0 <

<

. An example is provided to illustrate the results.