  The cosmology of branes undergoing the self-tuning mechanism of the
cosmological constant is considered. The equations and matching conditions are
derived in several coordinate systems, and an exploration of possible solution
strategies is performed. The ensuing equations are solved analytically in the
probe brane limit. We classify the distinct behavior for the brane cosmology
and we correlate them with properties of the bulk (static) solutions. Their
matching to the actual universe cosmology is addressed.
