Abstract In this paper we consider a nonlinear system of algebraic equations. We give sufficient conditions which imply the existence and uniqueness of positive solutions of the system. Our theorem extends earlier results known in the literature. Several examples illustrate the main result. Nonlinear or linear algebraic systems appear as steady-state equations in continuous and discrete dynamical models (e.g., reaction–diffusion equations [14,19], neural networks [5, 6,15,22] compartmental systems [2,4,11,12,16,17], population models [13,21]). Next we mention some typical models. Compartmental systems are used to model many processes in pharmacokinetics, metabolism, epidemiology and ecology. We refer to [16,17] as surveys of basic theory and applications of linear and nonlinear compartmental systems without and with delays.