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Control systems with transport lag are commonly encountered, and the presence of nonlinearities in such systems makes stability analysis difficult. Parameter plane equations for such systems are formulated and used to map the imaginary axis of the s plane onto the parameter plane. Stability conditions are studied for a system with transport lag and one single-valued nonlinearity and also for a system with transport lag and a hysteretic-type non-linearity. In both cases the existence and characteristics of limit cycles are studied. Application of the method is made to an aircraft pitch control system.