Let θ be a parameter vector of a multidimensional stochastic process belonging to the exponential class. In order to get unbiased and efficient estimators ϕ for certain vector-valued functions h(θ) sequential procedures we often used. In this note some properties of such efficient sequential estimators are studied: consistency, asymptotical normality and completeness. A method for finding minimal-variance unbiased sequential estimators conclude the paper.