  The obstructions to the existence of a hierarchy of hydrodynamic conservation
laws are studied for a multicomponent dispersionless KdV system. It is shown
that if an underlying algebra is Jordan, then the lowest obstruction vanishes
and that all higher obstructions automatically vanish. Deformations of these
multicomponent dispersionless KdV-type equations are also studied. No new
obstructions appear, and hence the existence of a fully deformed hierarchy
depends on the existence of a single purely hydrodynamic conservation law.
