We present Very Large Array (vla) and Westerbork Synthesis Radio Telescope (wsrt) 21-cm Hi observations of 19 late-type low surface brightness (LSB) galaxies. Our main findings are that these galaxies, as well as having low surface brightnesses, have low Hi surface densities, about a factor of ~ 3 lower than in normal late-type galaxies. We show that LSB galaxies in some respects resemble the outer parts of late-type normal galaxies, but may be less evolved. LSB galaxies are more gas-rich than their high surface brightness counterparts. The rotation curves of LSB galaxies rise more slowly than those of HSB galaxies of the same luminosity, with amplitudes between 50 and 120 km s−1, and are often still increasing at the outermost measured point. The shape of the rotation curves suggests that LSB galaxies have low matter surface densities. We use the average total mass surface density of a galaxy as a measure for the evolutionary state, and show that LSB galaxies are among the least compact, least evolved galaxies. We show that both MHI/LB and Mdyn/LB depend strongly on central surface brightness, consistent with the surface brightness–mass-to-light ratio relation required by the Tully-Fisher relation. LSB galaxies are therefore slowly evolving galaxies, and may well be low surface density systems in all respects.