A procedure is proposed for the probabilistic analysis of nonlinear structures. Governing equations expressed in incremental forms for random structures subjected to random loads are derived from a nonlinear theory of structural analysis and the second moment method in probability theory. An incremental load procedure with a Newton-Raphson type of iteration scheme is used to solve the governing equations for obtaining probabilistic moments of displacements and tracing the load-displacement curve. Probabilistic moments of member forces which can be used in structural reliability analysis are inferred from those of system parameters and loads via the present probabilistic structural analysis method. The utilization of the present approach is demonstrated by the analysis of nonlinear elastic plane frames. The feasibility of the proposed method and its application to structural reliability are illustrated by means of several examples.