This paper considers the optimal design problem for multiresponse regression models. The <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$R$$</EquationSource> </InlineEquation>-optimality introduced by Dette (J R Stat Soc B 59:97–110, <CitationRef CitationID="CR5">1997</CitationRef>) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the <InlineEquation ID="IEq5">...</inlineequation></citationref></equationsource></inlineequation>