  It is shown that the generalized Riemann equation is equivalent with the
multicomponent generalization of the Hunter - Saxton equation. New matrix and
scalar Lax representation is presented for this generalization. New class of
the conserved densities, which depends explicitly on the time are obtained
directly from the Lax operator. The algorithm, which allows us to generate a
big class of the non-polynomial conservation laws of the generalized Riemann
equation is presented. Due to this new series of conservation laws of the
Hunter-Saxton equation is obtained.
