Many pseudorandom sequence generators and stream ciphers are based on linear feedback shift registers with dynamic feedback (DLFSR) in order to increase the period and linear span of sequences. In this paper, we study the different modes of operation of the DLFSR structure and propose a general classification of the generators attending to the way in which the feedback is applied. A theoretical study of these modes of operation allows us to identify the optimal ones. Recent DLFSR proposals are identified as particular elements of the classification proposed, and a new generic pseudorandom sequence generator, belonging to one of the optimal classes, is presented.