What can we study through families and accompanied air showers?

At mountain altitudes, high energy gamma-ray bundles (gamma-rays in parallel trajectories and with the same direction of an air shower) can be observed in the central part of air showers. These gamma-ray bundles (greater than or equal to 1 TeV) and their associated air showers are observed simultaneously at Mt. Chacaltaya (5200 m) by our detectors. The gamma-ray bundle in the air shower can give information on the primary composition and the characteristics of proton interaction. In this paper, we report on experimental results, simulations calculated for the present experiments, and also problems in simulations.