In order to attenuate parainfluenza type 3 virus, a wild-type strain that was isolated from a child with respiratory disease was adapted to replicate in African green monkey kidney cells at 20.degree. C. Replication at 20.degree. C was not a property of the wild-type virus. The virus was serially passaged 45 times in the cold, and clones were selected following passage levels 7, 12, 18 and 45. The population of cold-adapted virus was found to be progressively enriched with temperature-sensitive (ts) mutants. After 7 passages in the cold, 1 of 9 clones was temperature-sensitive and, after 12 passages in the cold, 3 of 12 were. Following 18 passages in the cold, 80% of the clones were temperature-sensitive and, after 45 passages in the cold, all clones were temperature-sensitive. In addition to being temperature-sensitive each ts clone manifested the tiny plaque morphology. Each ts clone was also cold adapted. Some clones were cold adapted but were not temperature-sensitive. The mutants were found to be genetically stable when serially passaged at 32.degree., 35.degree. or 39.degree. C. The mutants may possess the necessary degree of attenuation for use as live attenuated intranasal vaccines.