In this paper we have defined two approaches to be error-robust when the precise form of error-structure is unknown. An experiment is optimal by the first criterion if it maximizes the minimum effciency over all candidates of error structure and is optimal by the second if it maximizes the minimum average of the efficiency over all candidates of error structure. In order to appreciate the basic implications of each design criterion, these approaches are applied to two different experimental situations, D- and heteroscedastic G-optimalities.