  In this paper, we study the Cauchy problem of a periodic 2-component
$\mu$-Hunter-Saxton system. We first establish the local well-posedness for the
periodic 2-component $\mu$-Hunter-Saxton system by Kato's semigroup theory.
Then, we derive precise blow-up scenarios for strong solutions to the system.
Moreover, we present a blow-up result for strong solutions to the system.
Finally, we give a global existence result to the system.
