Summary: Recent years have seen an increasing interest in the study of continuous-time computational models. However, not so much has been done with respect to setting up a complexity theoretic framework for such models. The present paper intends to go a step into this direction. We consider problems over the real numbers which we try to relate to Lyapunov theory for dynamical systems: The global minimizers of particular energy functions are supposed to give solutions of the problem. The structure of such energy functions leads to the introduction of problem classes \({\mathbf U}\) and \textbf{NU}; for the systems we are considering they parallel the classical complexity classes \({\mathbf P}\) and \textbf{NP}. We then introduce a notion of reducibility among problems and show existence of complete problems for \textbf{NU} and for \textbf{PU}, a polynomial hierarchy of continuous-time problems.