The longitudinal development of muons in air showers with primary energies in the range 1017-1018 eV has been studied by measuring the arrival time distributions in the Akeno air-shower array (930 g cm-2 atmospheric depth, 900 m above sea level). These arrival time distributions of muons with energies above 1.0 GeV are consistent with those expected from models of particle interactions with very high multiplicity at large core distances and, on the contrary, with those expected from the models with low multiplicity at small core distances. This implies that the longitudinal development at atmospheric depths smaller than 500 g cm-2 is very fast and that at larger atmospheric depths it is rather slow, in agreement with the conclusion on the longitudinal development of electrons derived from the arrival time distributions of atmospheric Cerenkov light measured in the Chacaltaya air-shower array as well as in the Akeno array. Comparison of the mean arrival times of muons with energies above 0.5 GeV and the calculation made by McComb et al. (1979) suggests that no serious contribution to the arrival time distributions of such muons is made by muons arising from photon-nucleus collisions.