We consider the problem of successive-refinement coding for lossy compression of individual sequences, namely, compression in two stages, where in the first stage, a coarse description at a relatively low rate is sent from the encoder to the decoder, and in the second stage, additional coding rate is allocated in order to refine the description and thereby improve the reproduction. Our main result is in establishing outer bounds (converse theorems) for the rate region where we limit the encoders to be finite-state machines in the spirit of Ziv and Lempel's 1978 model.The matching achievability scheme is conceptually straightforward. We also consider the more general multiple description coding problem on a similar footing and propose achievability schemes that are analogous to the well-known El Gamal-Cover and the Zhang-Berger achievability schemes of memoryless sources and additive distortion measures.