An extension of the stability-equation method for prediction of limit-cycles in nonlinear two-input two-output (TITO) control systems is presented. A system with two nonlinearities is considered first, then a system with four nonlinearities is analysed. The presented method is useful for preliminary analysis and design of automatic tuning of PID controllers for TITO processes with decentralised relay feedback. All the results are checked by computer simulations and comparisons with other methods in current literature are made.