since the predecessor to this volume (lnm 1186, eds. l. arnold, v. wihstutz)appeared in 1986, significant progress has been made in the theory and applications of lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. this volume opens with an introductory survey article (arnold/crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. from the contents: l. arnold, h. crauel: random dynamical systems.- i.ya. goldscheid: lyapunov exponents and asymptotic behaviour of the product of random matrices.- y. peres: analytic dependence of lyapunov exponents on transition probabilities.- o. knill: the upper lyapunov exponent of sl (2, r) cocycles:discontinuity and the problem of positivity.- yu.d. latushkin, a.m. stepin: linear skew-product flows and semigroups of weighted composition operators.- p. baxendale: invariant measures for nonlinear stochastic differential equations.- y. kifer: large deviationsfor random expanding maps.- p. thieullen: generalisation du theoreme de pesin pour l -entropie.- s.t. ariaratnam, w.-c. xie: lyapunov exponents in stochastic structural mechanics.- f. colonius, w. kliemann: lyapunov exponents of control flows.