  A new class of completely integrable models is constructed. These models are
deformations of the famous integrable and exactly solvable Gaudin models. In
contrast with the latter, they are quasi-exactly solvable, i.e. admit the
algebraic Bethe ansatz solution only for some limited parts of the spectrum. An
underlying algebra responsible for both the phenomena of complete integrability
and quasi-exact solvability is constructed. We call it "quasi-Gaudin algebra"
and demonstrate that it is a special non-Lie-algebraic deformation of the
ordinary Gaudin algebra.
