The A(1)Sigma(+) <- X-1 Sigma(+) band system in the (KLi)-K-39-Li-7 molecule is investigated by the polarisation labelling spectroscopy technique. The excited state is characterised by a set of Dunham coefficients describing rovibrational levels v = 0-34; J = 9-73 and the corresponding potential energy curve is constructed with the Rydberg-Klein-Rees method. The main equilibrium constants are T-e - 12097: 11(3) cm(-1), ( with respect to the minimum of the electronic ground state), omega(e) 137.0821(131) cm(-1); R-e = 3.9466(3) angstrom. (C) 2012 Elsevier B. V. All rights reserved.