The one-pion and two-pion production in the p(α, α ′ )X reaction at an energy of E α = 4.2 GeV has been studied by simultaneous registration of the scattered α ′ particle and the secondary proton or pion. The obtained results demonstrate that the inelastic α-particle scattering on the proton at the energy of the experiment proceeds either through excitation and decay of the ∆ resonance in the projectile α particle, or through excitation in the target proton of the Roper resonance, which decays mainly on a nucleon and a pion or a nucleon and a σ meson -a system of two pions in the isospin I = 0, S-wave state.A study of inelastic αp scattering at an energy of ∼ 1 GeV/nucleon is of significant interest since it is related, in particular, to the problem of the N(1440)P 11 (Roper) resonance. The Roper resonance [1] is the lowest positive-parity excited state N * of the nucleon, and in many respects it is a very intriguing and important resonance. Morsch et al. [2,3] have interpreted the excitation of the Roper resonance in inelastic αp scattering as the breathing-mode (L = 0) monopole excitation of the nucleon. In this interpretation, the N(1440) resonance mass is related to the compressibility of the nuclear matter (on the nucleonic level). This resonance also plays an important role in many intermediate-energy processes, in the threebody nuclear forces and in the swelling of nucleons in nuclei. The investigation of the N(1440) resonance was the goal of numerous theoretical and experimental studies. This activity was motivated by the still not properly understood nature of the resonance, its relatively low mass and anomalously large width of a few hundred MeV.The Roper resonance was observed and studied for the first time in the πp scattering partial-wave analyses [1,[4][5][6][7]. The fact that the Roper resonance is also strongly excited in αp scattering was quite puzzling. To understand the excitation of this resonance in different reactions, Morsch and Zupranski [3] performed a combined analysis of the data of πN-, αp-and γp-scattering experiments, with the conclusion that the N(1440) state represents a structure formed of two resonances, one understood as the nucleon breathing mode and the other one as an excited state of the ∆ 3,3 (1232) (∆) resonance. The first resonance is strongly excited by scalar probes, like in αp scattering, whereas the second one is excited in spin-isospin-flip reactions, like in πN scattering. The two-resonance picture of N(1440) and the breathing-mode excitation of the proton was also discussed by the same authors [8] in a reanalysis of high-energy pp-and πp-scattering data.An advantage of studying the Roper resonance in an αp-scattering experiment, as compared to πN, NN and γN experiments, is that in the case of αp scattering the number of the reaction channels is rather limited. At an energy of ∼ 1 GeV/nucleon, the Roper resonance is strongly excited in αp scattering, whereas the contribution from excitation of other baryon resonances is expected to be small [9].Inelastic αp scatteri...