We have considered two distant mesoscopic superconducting quantum interference device (SQUID) rings A and B in the presence of two-mode nonclassical state fields and investigated the correlation of the supercurrents in the two rings using the normalized correlation function CAB. We show that when the parameteris very small for the separable state with the density matrix ˆ � = (|�, −�i h �, −�| + |−�,�i h− �,�|)/2 and entangled coherent state (ECS) |ui = N1(|�, −�i + |−�,�i ) fields, the dynamic behaviours of the normalized correlation function CAB are similar, but it is quite different for the entangled coherent state |ui = N2(|�, −�i − |− �,�i ) field. When the parameteris very large, the dynamic behaviours of CAB are almost the same for the separable state, entangled coherent state |ui and |ui fields. For the two-mode squeezed vacuum state field the maximum of CAB increases monotonically with the squeezing parameter r, and as r → ∞, CAB → 1. This means that the supercurrents in the two rings A and B are quantum mechanically correlated perfectly. It is concluded that not all the quantum correlations in the two-mode nonclassical state field can be transferred to the supercurrents; and the transfer depends on the state of the two-mode nonclassical state field prepared.