A series of recently conducted experiments (1-4) have revealed the following important characteristics of the prompt muon production in the forward direction in protonnucleus collisions at high energies: i) the measured V/r: ratio has been, in almost all the cases, of the order of 10 -5. ii) The ratio of prompt positive and negative muons is about 1. iii) The muons are originated in pairs, iv) The V/r: ratio depends on the outgoing-muon momentum, with the direct production rising slowly with increasing transverse momentum (a). We propose to explain here the above-mentioned features of the prompt muon production with the help of a multiple-production model based on a certain kind of lepton-hadron relation. No theoretical model has yet a t tempted-le t alone succeeded--to explain these observations. Side by side, on the basis of the available data there is an important and prospective speculation about the possibilities of copious direct photon production which is supposed to be a possible clue to or a resolution of the afore-mentioned prompt muon puzzle. It has been proposed by FARRAR and ]~RAUTSCHI (5) that all direct leptons not due to vector-meson decay can be at tr ibuted to the decay of virtual photons. Though the detailed behaviour of the y/r: ratio could not be predicted it has been shown there that the expected value of the ratio at large PT is of the order of 10 -1 and falls to 10 -~ at the 1OW-pT region. In case of inclusive production, BEI]~R et al. (e) have, however, reported to the contrary: the ratio (y/r:) is 15 at low PT and falls to zero at high PT.