  We give the Lax representations for for the elliptic, hyperbolic and
homogeneous second order Monge-Ampere equations. The connection between these
equations and the equations of hydrodynamical type give us a scalar
dispersionless Lax representation. A matrix dispersive Lax representation
follows from the correspondence between sigma models, a two parameter equation
for minimal surfaces and Monge-Ampere equations. Local as well nonlocal
conserved densities are obtained.
