We introduce a class of quantum integrable systems generalizing the Gaudin
model. The corresponding algebras of quantum Hamiltonians are obtained as
quotients of the center of the enveloping algebra of an affine Kac-Moody
algebra at the critical level, extending the construction of higher Gaudin
Hamiltonians from hep-th/9402022 to the case of non-highest weight
representations of affine algebras.