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In this paper we study a ratio-dependent predator-prey model with a freeboundary causing by both prey and predator over a one dimensional habitat. Westudy the long time behaviors of the two species and prove aspreading-vanishing dichotomy, namely, as t goes to infinity, both prey andpredator successfully spread to the whole space and survive in the newenvironment, or they spread within a bounded area and die out eventually. Thenthe criteria governing spreading and vanishing are obtained. Finally, whenspreading occurs, we provide some estimates to the asymptotic spreading speedof h(t).

A Free Boundary Problem with a Stefan Condition for a Ratio-dependent Predator-prey Model