  In this paper, a two-component variant of the Degasperis-Procesi equation on
the real line is discussed. Applying Kato's theory, we first prove the local
well-posedness for the equation under consideration in $H^s\times H^{s-1}$, for
$s\geq 2$. Second we establish the precise blow-up scenario. For compactly
supported initial data, we show that the associated solution does not have
compact support for any positive time; the localized initial disturbance
propagates with an infinite speed. Although the solution is no longer compactly
supported we prove that it decays at an exponentially fast rate for the
duration of its existence.
