  We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled
to bosons and fermions in the fundamental representation. Extending an approach
due to Rajeev we show that the limiting theory can be described as a classical
Hamiltonian system whose phase space is an infinite-dimensional
supergrassmannian. The linear approximation to the equations of motion and the
constraint yields the 't Hooft equations for the mesonic spectrum. Two other
approximation schemes to the exact equations are discussed.
