  We construct six multi-parameter families of Hermitian quasi-exactly solvable
matrix Schroedinger operators in one variable. The method for finding these
operators relies heavily upon a special representation of the Lie algebra
o(2,2) whose representation space contains an invariant finite-dimensional
subspace. Besides that we give several examples of quasi-exactly solvable
matrix models that have square-integrable eigenfunctions. These examples are in
direct analogy with the quasi-exactly solvable scalar Schroedinger operators
obtained by Turbiner and Ushveridze.
