This is an old paper put here for archeological purposes. We compute the second cohomology of current Lie algebras of the form $Lotimes A$, where $L$ belongs to some class of Lie algebras which includes classical simple and Zassenhaus algebras, and o
f some modular semisimple Lie algebras. The results are largely superseded by subsequent papers, though, perhaps, some tricks and observations used here remain of minor interest.
