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The problem of smooth receding contact between an orthotropic layer and an orthotropic half-space has been considered in this papaer. The paper includes a generalization of the results of the paper by L. M. KEER, J. DUNDURS, K. C. TSAI [4] concerning receding contact between an isotropic layer and an isotropic half-space. It is observed that the task of finding the extent of contact in the loaded configuration can be reduced to an eigenvalue problem of a homogenous Fredholm integral equation. The kernel of the Fredholm integral equation is found to be dependent on the elastic constants of the layer but is independent of the elastic constants of the half-space below, which is in contrast to the study for the isotropic materials, where the kernel is independent of the elastic constants. Finally some numerical results have been presented in graphs in order to compare the results of interest for isotropic and orthotropic materials.