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The kinematics of generalized continua is investigated and key points concerning the definition of overall tangent strain measure are put into evidence. It is shown that classical measures adopted in the literature for micromorphic continua do not obey a constraint qualification requirement, to be fulfilled for well-posedness in optimization theory, and are therefore termed redundant. Redundancy of continua with latent microstructure and of constrained Cosserat continua is also assessed. A simplest, non-redundant, kinematic model of micromorphic continua, is proposed by dropping the microcurvature field. The equilibrium conditions and the related variational linear elastostatic problem are formulated and briefly discussed. The simplest model involves a reduced number of state variables and of elastic constitutive coefficients, when compared with other models of micromorphic continua, being still capable of enriching the Cauchy continuum model in a significant way

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