We have followed the evolution of the superconductingTc on intercalation of Li in ZrSe2 by means of magnetization studies at very low temperatures. To interpret the electronic structure and instabilities, we present the results of extensive LMTO-ASA band structure calculations on ZrSe2 and the idealized compound LiZrSe2 . The experimental results suggest a picture of phase segregation in the intercalated samples into regions where Li atoms are a part of the percolating cluster and regions where the Li are not. The electronic structure calculations help to understand the nature of the bonding in this system and in particular, the nature of instabilities on the Fermi surface in the intercalated compounds. In keeping with certain models for the occurrence of superconductivity in systems whose electronic structures combine localized and itinerant behaviour, the title compounds display regions of high and low dispersion in the Fermi surface. A comparison with the superconducting spinel LiTi2O4 is particularly fruitful.