We observed nearby (D < 10 Mpc) galaxies (Henize 2-10, IC 10, IC 342, M 83, NGC 253 and NGC 6946) in the rotational lines of carbon monoxide CO and in the fine-structure transitions of atomic carbon [CI] with the Caltech Submillimeter Observatory (CSO). Using our new data, those from the literature and the LVG and PDR models, we derived the physical properties of the warm and dense molecular gas (kinetic temperature, UV radiation field, gas density...) in each nucleus. We predicted lines intensities for the 12CO(5-4), 12CO(7-6) and 12CO(8-7) lines which are, even now, still difficult or impossible to detect from the ground but will become available in few years with ALMA and HIFI or PACS, on board the Herschel satellite. Studying the ISM of nearby galaxies, we provide a first step in the understanding of the ISM processes in more distant galaxies.