Properties of gamma -ray families in the cosmic radiation are simulated for a variety of assumptions about the characteristics of high-energy interactions. It is shown that the frequencies of the families observed experimentally are significantly lower than those expected on the basis of extrapolation of high-energy interaction characteristics and the primary mass composition. This result confirms the extensive air shower observation of rapid development of cascades in the upper atmosphere. The phenomenon can be understood if the multiplicity of secondary particles increases more rapidly with energy than is normally assumed.