  In this paper we consider a two-component system of the Holm-Staley equation
with no stretching and a one-parameter nonlinearity in the convection term.
Point symmetries are found, conditions for the existence of multipeakon and
multikink solutions are determined. Solutions for the 1-peakon and 1-kink are
explicitly obtained and they exhibit a behaviour quite different of their
analogous in the scalar equation.
