The failure and repair of two homogeneous classes of components under the Markov regime is considered; the priority class containing N1 components and the ordinary class containing N2 components. The class of N1 components has nonpreemptive priority over the other class. In particular, the head-of-the-line priority discipline has been assumed. Under the same operating conditions, the steady-state availability was found to be highest when the components with the smallest failure rate have priority over the others. The priority assignment of the components with the highest failure rate maximizes the repairman efficiency.