  According to the Goldstone theorem a scalar theory with a spontaneously
broken global symmetry contains strictly massless states. In this letter we
identify a loophole in the current-algebra proof of the theorem. Therefore, the
question whether in models with Mexican hat potential the tangential
excitations are strictly massless or are just almost massless as compared to
the radial ones remains open. We also argue that mass of the tangential
excitations approaches zero even if the symmetry is not spontaneously broken
but a combination of the field components invariant under the symmetry
transformations acquires a large vacuum expectation value.
