The photoluminescence (PL) of InAlAs grown on InP has been studied in a wide range of temperatures and excitation intensities. A novel emission ascribed to the presence of defects has been found by about 120-180 meV below the near band edge (NBE) line. The novel wide PL band is observed in the spectra only in a limited range of temperatures of 50-160 K, and is seen neither at liquid helium nor at room temperatures. The analysis of the PL behaviour with sample temperature and excitation power together with non-stationary PL kinetics allows us to conclude that both the NBE PL and the novel PL band are controlled by transitions via states of band tails formed due to alloy disorder in these films. The NBE PL is caused by recombination of carriers in the band tails, while deep levels related to defects and located in the same regions as the deepest band tail states are supposedly involved in the defect-related PL transitions. We demonstrate that no defect-related PL is found in the spectra if quasi-stoichiometric growth conditions were used during film growth, which resulted in a PL efficiency by about 1-2 orders of magnitude greater than that of samples grown under more common As-rich conditions.