In this paper, various replacement policies for the general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. In this model, when the unit fails at its age t, Type I failure occurs with probability 1-p(t) and Type II failure occurs with probability p(t), $0{leq}p(t){leq}1$. Under the model, optimal replacement policies for the long-run average cost rate and the limiting efficiency are considered. Also taking the cost and the efficiency into consideration at the same time, the properties of the optimal policies under the Cost-Priority-Criterion and the Efficiency-Priority-Criterion are obtained.