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In this paper optimal experimental designs for inverse quadratic regressionmodels are determined. We consider two different parameterizations of the modeland investigate local optimal designs with respect to the $c$-, $D$- and$E$-criteria, which reflect various aspects of the precision of the maximumlikelihood estimator for the parameters in inverse quadratic regression models.In particular it is demonstrated that for a sufficiently large design spacegeometric allocation rules are optimal with respect to many optimalitycriteria. Moreover, in numerous cases the designs with respect to the differentcriteria are supported at the same points. Finally, the efficiencies ofdifferent optimal designs with respect to various optimality criteria arestudied, and the efficiency of some commonly used designs are investigated.

Optimal experimental designs for inverse quadratic regression models