Because optical wavelength division multiplexing (WDM) networks are expected to be realized for building up backbone in the near future, multicasting in WDM networks needs to be addressed for various network applications. This paper studies an extended multicast routing and wavelength assignment (RWA) problem called multicast routing and wavelength assignment with delay constraint (MRWA-DC) that incorporates delay constraints in WDM networks having heterogeneous light splitting capabilities. The objective is to find a light-forest whose multicast cost, defined as a weighted combination of communication cost and wavelength consumption, is minimum. An integer linear programming (ILP) model is proposed to formulate and solve the problem. Experimental results show that using CPLEX to solve the ILP formulation can optimally deal with small-scale networks. Therefore, we develop a heuristic, near-k-shortest-path heuristic (NKSPH), to solve the problem in large-scale networks. Numerical results indicate that the proposed heuristic algorithm can produce approximate solutions of good quality in an acceptable time.