  For higher genus multi-point current algebras of Krichever-Novikov type
associated to a finite-dimensional Lie algebra, local Lie algebra two-cocycles
are studied. They yield as central extensions almost-graded higher genus affine
Lie algebras. In case that the Lie algebra is reductive a complete
classification is given. For a simple Lie algebra, like in the classical
situation, there is up to equivalence and rescaling only one non-trivial
almost-graded central extension. The classification is extended to the algebras
of meromorphic differential operators of order less or equal one on the
currents algebra.
