We provide an extension of the Condorcet Theorem. Our model includes both the Nitzan-Paroush framework of "unequal competencies" and Ladha's model of "correlated voting by the jurors". We assume that the jurors behave "informatively", that is, they do not make a strategic use of their information in voting. Formally, we consider a sequence of binary random variables X=(X1,X2,...,Xn,...) with range in {0,1} and a joint probability distribution P. The pair $(X,P)$ is said to satisfy the "Condorcet Jury Theorem" (CJT) if, as n goes to infinity, the probability of having a majority of X's with value 1 goes to one.For a general (dependent) distribution P we provide necessary as well as sufficient conditions for the CJT. In particular, our results establishes the validity of the CJT for a domain which strictly (and naturally) includes the domain of independent jurors.