The location of energy minima on the conformational energy surface of molecules by computational methods (conformational searching) continues to play a key role in computer-assisted molecular modeling. Although a number of conformational search procedures have been devised over the past several years, new more efficient methods are urgently needed if molecules with increased complexity are to be treated in a quantitative manner. In this paper we describe a method, termed low-mode search (LMOD), which is based on eigenvector following (or mode following), for the exhaustive exploration of the potential energy hypersurface of molecules. It is particularly efficient at searching the conformational space of both cyclic and acyclic molecules, and we describe its effectiveness for a number of conformational search problems including acyclic, monocyclic, and bicyclic hydrocarbons and cyclic pentapeptides. No special treatment of rings in cyclic molecules is necessary, nor is it necessary to define rotatable bond...