Two dimensional non-linear multivariable systems with single valued non-linearities are analysed for stability, by replacing the non-linearities by their describing functionsN1andN2. Symmetric systems can be analysed easily as the characteristic equation can be factoriozed and the Nyquist criterion helps to find the existence of the limit cycle in the system. In the antisymmetric case, the characteristic equation is partitioned into real and imaginary parts and these are solved forN1, andN2and are plotted in theN1versusN2plane. The existence of the limit cycle is indicated by intersection of certain curves (at the same frequency) in theN1-N1plane. The stability of the limit cycle is determined by the perturbation technique.