A pipe coupling wherein a composite housing surrounds the objects or parts to be coupled with one another. The housing confines two annular gripping members, one for each part and each having a trapeziform cross-sectional outline with two oppositely inclined legs flanking an annular web which can be biased toward the respective part by a set of screws mating with the housing. The radially innermost portions of the legs have teeth which penetrate into the material of the respective parts to hold the parts against axial movement relative to each other. Each gripping member can be received in a discrete groove which has a trapeziform cross-sectional outline and is bounded in part by two oppositely inclined flanks whose inclination with reference to the axis of the housing is more pronounced than the inclination of the legs on the gripping members. The teeth of the legs of the gripping members are immediately adjacent the respective flanks. Alternatively, both gripping members can be installed in a common groove of the housing.