This paper is concerned with the three-dimensional initial boundary-value problem for the equations of magnetohydrodynamics with additional nonlinear terms stemming from a more general relationship between the electric field and the current density. The problem governs the motion of a viscous incompressible conducting liquid in a bounded container with an ideal conducting surface. The existence of a solution which is close to a certain basic solution is proved. The solution is found in the anosotropic Sobolev spaces $W^{2,1}_p$ with $p>5/2$. The proof relies on the theory of general parabolic initial boundary-value problems. Bibliography: 16 titles.