  We present numerical evidence for the existence of stationary spinning
generalizations for the static sphaleron in the Weinberg-Salam theory. Our
results suggest that, for any value of the mixing angle $\thetw$ and for any
Higgs mass, the spinning sphalerons comprise a family labeled by their angular
momentum $J$. For $\thetw\neq 0$ they possess an electric charge $Q=eJ$ where
$e$ is the electron charge. Inside they contain a monopole-antimonopole pair
and a spinning loop of electric current, and for large $J$ they show a
Regge-type behavior. It is likely that these sphalerons mediate the topological
transitions in sectors with $J\neq 0$, thus enlarging the number of transition
channels. Their action {\it decreases} with $J$, which may considerably affect
the total transition rate.
