AbstractWe present a project that aims to provide a complete theoretical and observational framework for an as yet unexplored class of variable stars, the ultralong-period Cepheids (P longer than 80–100 days). Given their very high luminosities (M_V up to −7 mag), with the Hubble Space Telescope we will be able to observe them easily in stellar systems located at large distances (~ 100 Mpc). This limit will be further increased, out to the Hubble flow (~ 350 Mpc), using future ground-based facilities such as the European Extremely Large Telescope. The nature of their pulsation is as yet unclear, as is their evolutionary status, which seems different from the central helium-burning phase generally associated with classical Cepheids. These objects have been found to cover a very large metallicity range, from [Fe/H] ~ −2 dex to solar values, and they are located in heterogeneous stellar systems, from dwarf to spiral galaxies. Once completely characterized, they could provide a crucial test, since they have been found in all Type Ia supernova host spiral galaxies that have been monitored for variability over long periods and that currently offer sound constraints on the estimated value of the Hubble constant.