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In this paper we consider Poisson loglinear models with linear constraints (LMLC) on the expected table counts. Multinomial and product multinomial loglinear models can be obtained by considering that some marginal totals (linear constraints on the expected table counts) have been prefixed in a Poisson loglinear model. Therefore with the theory developed in this paper, multinomial and product multinomial loglinear models can be considered as a particular case. To carry out inferences on the parameters in the LMLC an information-theoretic approach is followed from which the classical maximum likelihood estimators and Pearson chi-square statistics for goodness-of fit are obtained. In addition, nested hypotheses are proposed as a general procedure for hypothesis testing. Through a simulation study the appropriateness of proposed inference tools is illustrated.