The polarisation labelling spectroscopy technique is employed to study the 6(1)Pi <- X-1 Sigma(+) and 7(1)Pi <- X-1 Sigma(+) band systems of the KLi molecule located in the UV range. The Dunham coefficients derived for both previously unobserved excited states and potential energy curves constructed by the RKR method are compared with the recent theoretical calculations. A possibility of accessing triplet states of KLi via perturbations in the 6(1)Pi state is discussed. (C) 2008 Elsevier B.V. All rights reserved.