The properties of travelling- and standing-wave resonators and their i
nfluence on the modal composition and propagation of transverse patter
ns are analysed and a prescription for constructing a travelling-wave
resonator 'equivalent' to a standing-wave resonator is given. It is sh
own that the presence of an intracavity nonlinear medium invalidates t
he equivalence between the two kinds of cavity, even when the interfer
ence between the counterpropagating waves can be neglected. Therefore
great care has to be taken when comparing experimental and theoretical
results obtained in different types of cavity, since in general their
properties differ. Some implications concerning the appearance of pha
se singularities in the two kinds of resonator are discussed.