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We extend the definition of quantum discord as a quantifier of nonClassical correlations in a quantum state to the case where weak measurements are performed on subsystem A of a bipartite system AB. The properties of weak discord are explored for several families of quantum states. We find that in many cases weak quantum discord is identical to normal discord and in general the values of the two are very close to each other. Weak quantum discord reduces to discord in the appropriate limits asarXiv:1511.09224v1 fatcat:w7tvd76sercuzme66pvtqew3ya