In many experimental situations, especially in engineering, pharmaceutical and biomedical as well as environmental research, there are more than one response to be measured for each unit. The multiresponse models play an important role in many areas of science. This work deals with optimal design problems for the multiresponse linear models. We focus on investigating the optimality, admissibility and invariance of approximate designs. Necessary and sufficient conditions are given for a design to be admissible and invariant. An Elfving's theorem for D-optimality is established for the multiresponse linear models. Several examples are given for illustration.

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