This talk concentrates on the model-robust design problem for multiresponse model with possible bias. We assume that the fitted model for each response is first-degree or second-degree polynomials and we confine ourselves to the use of the generalized least squares estimates for the unknown parameters. We assume that the model bias includes the effects due to higher degree terms of multivariate Hermite polynomials. A criterion for choosing designs is proposed based on averaging the mean squared error over all possible bias. It is shown that the criterion is invariant with respect to orthogonal transformation of designs. Several illustrative examples are presented.