Abstract <p>The article presents the first results of a study of unstable nuclear states arising in the processes of α fragmentation of ¹²C and ¹⁶O nuclei in nuclear photoemulsion under the action of relativistic charged hadrons with a momentum of 7 GeV/<i>c</i>. The experimental technique is based on the identification of events with the production of at least three short-range α particles, which makes it possible to perform a full kinematic reconstruction of the events under conditions of 4π detection geometry. Owing to precision coordinate measurements of α-particle tracks in nuclear emulsion, their full ranges and emission angles were determined, and their kinetic energies were reconstructed. On this basis, the invariant masses of α-particle pairs and triplets were obtained for each event. The analysis of the invariant mass spectra provided a quantitative estimate of the probability of formation of low-lying excited states of ⁸Be and ¹²C nuclei and demonstrated the prospects for further investigation of α-particle dissociation of ¹²C and ¹⁶O nuclei using the nuclear photoemulsion method with significantly higher statistics, which is expected to be achieved with the aid of a robotic microscope with automatic image processing.</p>