Abstract We propose a simple analytic theory for environmentally dependent molecular cloud lifetimes, based on the large-scale (galactic) dynamics of the interstellar medium. Within this theory, the cloud lifetime is set by the time-scales for gravitational collapse, galactic shear, spiral arm interactions, epicyclic perturbations, and cloud–cloud collisions. It is dependent on five observable quantities, accessible through measurements of the galactic rotation curve, the gas and stellar surface densities, and the gas and stellar velocity dispersions of the host galaxy. We determine how the relative importance of each dynamical mechanism varies throughout the space of observable galactic properties, and conclude that gravitational collapse and galactic shear play the greatest role in setting the cloud lifetime for the considered range of galaxy properties, while cloud–cloud collisions exert a much lesser influence. All five environmental mechanisms are nevertheless required to obtain a complete picture of cloud evolution. We apply our theory to the galaxies M31, M51, M83, and the Milky Way, and find a strong dependence of the cloud lifetime upon galactocentric radius in each case, with a typical cloud lifetime between 10 and 50 Myr. Our theory is ideally suited for systematic observational tests with the Atacama Large Millimetre/submillimetre array.