Values of λ are determined for which there exist positive solutions of the system of dynamic equations, u Δ Δ ( t ) + λ a ( t ) f ( v ( σ ( t ) ) ) = 0 , v Δ Δ ( t ) + λ b ( t ) g ( u ( σ ( t ) ) ) = 0 , for t ∈ [ 0 , 1 ] T , satisfying the boundary conditions, u ( 0 ) = 0 = u ( σ 2 ( 1 ) ) , v ( 0 ) = 0 = v ( σ 2 ( 1 ) ) , where T is a time scale. A Guo-Krasnosel'skii fixed point-theorem is applied.