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We propose factorized difference operators L(u) associated with the twistedquantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}),U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to beannihilated by a screening operator. Based on a basis of the solutions of thedifference equation L(u)w(u)=0, we also construct a Casorati determinantsolution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).

Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras