A kind of two-parameter correlated negative binomial state is construc
ted and analysed from the point of view of quantum optics theory in tw
o-mode Fock space. By choosing a suitable two-mode correlated Holstein
-Primakoff-analogue transformation, the state can be identified as a t
ype of correlated SU (1, 1) coherent state. The possible physical uses
of the state are also pointed out.