Abstract Generally, it is very difficult to derive optimal or at least efficient designs for linear models with correlated observations, and for some correlation structure, an exact D -optimal design does not exist. In this paper we have developed the notion of a D - optimal robust first order design ( D -ORFOD) for linear model with a general correlated error structure. We have shown that D -optimal robust first order designs are always robust first order rotatable designs (RFORDs) but the converse is not always true. For a first order linear model with autocorrelated error, we have developed a set of efficient RFORDs with efficiency around ninety percent and the developed designs are very close to D -ORFODs. We have also developed a new method of analysis that is the estimation of regression parameters, correlation parameter and error variance, assuming the correlation parameter involved in the correlation structure is unknown.