In many multi-loop nonlinear systems, it is possible to get from the original set of simultaneous differential equations a single differential equation of a higher order. The high order nonlinear differential equa- tion can be solved by an n -dimensional phase-space method, which is an extension of the phase-plane method. As an illustration, a three- loop system is analyzed. Numerical examples for a two-loop system with nonlinear elements either in one of the loops or in the coupling are also given. Two-dimensional trajectories are shown as projections of phase-space trajectories.