Recently, Grassberger [1997, Phys. Rev. E, 56, 3682] has presented a new algorithm ('PERM') for simulating flexible polymer chains. This algorithm has been shown to have a good efficiency and has been used in a wide class of systems. A drawback of this algorithm is that it is static: it is therefore not suited for Markov-chain Monte Carlo simulations. Here, we present a dynamic generalization of the PERM algorithm. For a specific example, we compare the efficiency of DPERM to that of other Monte Carlo algorithms. In the case studied, we find that DPERM is only marginally more efficient. However, this result may depend on the details of the implementation.