An analytical expression for the condition of existence of limit-cycle behaviour for a class of third-order non-linear control systems with memory-type non-linearity is derived. The criteria for the stability of the limit cycle are also included. A typical example is taken for the purpose of illustrating the method of finding the limit-cycle parameters. The divergent, convergent and semistable equilibrium points on the F(a,b,α,β)/E plane are clearly defined.