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In this paper, we give a parametrization of asymptotic Jenkins–Strebel rays. It is a kind of global coordinates of the Teichmüller space. For any admissible curve family of a surface, the subset of the boundary of the Teichmüller space which is constructed by pinching of the given curve family can be determined. There exists a homeomorphism of the product of the boundary space and several parameter spaces onto the Teichmüller space such that each family of asymptotic Jenkins–Strebel rays is represented by the parameters. The idea is obtained by [MM75].

A global coordinate of the Teichmüller space related to asymptotic Jenkins–Strebel rays