  It is argued that two-dimensional U(N) spin models for any N undergo a
BKT-like phase transition, similarly to the famous XY model. This conclusion
follows from the Berezinskii-like calculation of the two-point correlation
function in U(N) models, approximate renormalization group analysis and
numerical investigations of the U(2) model. It is shown, via Monte Carlo
simulations, that the universality class of the U(2) model coincides with that
of the XY model. Moreover, preliminary numerical results point out that
two-dimensional SU(N) spin models with the fundamental and adjoint terms and
N>4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models.
