  We define genuine total, classical and quantum correlations in tripartite
systems. The measure we propose is based on the idea that genuine tripartite
correlation exists if and only if the correlation between any bipartition does
not vanish. We find in a symmetrical tripartite state, for total correlation
and classical correlation, the genuine tripartite correlations are no less than
pair-wise correlations. However, the genuine quantum tripartite correlation can
be surpassed by the pair-wise quantum correlations. Analytical expressions for
genuine tripartite correlations are obtained for pure states and rank-2
symmetrical states. The genuine correlations in both entangled and separable
states are calculated.
