This paper proposes a new method to compute alternate routes for multiple fault tolerance on Dynamic WDM Optical Networks. The method allows to obtain all the paths that replace the primary routes affected by one or several failures. Additional paths, called secondary routes, are used to keep each user connected to the network, including cases where multiple simultaneous link failures occur. The method also allows to obtain the number of wavelengths in each link of the network, computed such that the blocking probability of each connection is less than a pre-defined threshold (which is a network design parameter), in spite of the occurrence of k simultaneous link failures, with k ≥ 1. The solution obtained by the new algorithm is significantly more efficient than the result of applying current methods, its implementation is notably simple and its on-line operation is very fast.