The present article reports on an analysis of the properties that gamma-ray families featuring a halo exhibit in the cores of extensive air showers (EAS). The events under analysis were obtained in the XREC (x-ray emulsion chambers) PAMIR experiment, and the properties of these events were studied at distances extending up to about 10 cm from the EAS axis with a resolution of approximately 30 $$\mu$$ m. The investigation of the parameters of events in EAS cores by the halo method permitted analyzing the mass composition of primary cosmic radiation (PCR) at $$E_{0}=10$$ PeV and assessing the fraction of light nuclei in PCR, which depend only slightly on the model of EAS propagation through the atmosphere. From an analysis of gamma-ray families featuring a halo and multicenter halos obtained in the PAMIR XREC, it was found that the fraction of the ( $$p+\textrm{He}$$ ) component of PCR was about 40 $${\%}$$ . The properties of proton-induced EAS events detected at the Tien-Shan high-mountain Scientific Station (TShSS) were studied along with the KASCADE-Grande experimental data. On the basis of studying the dependence of the EAS age and $$N_{\mu}$$ on $$N_{e}$$ in the TShSS EAS (EAS $$+$$ XREC TShSS) data, it is concluded that PCR mass composition becomes heavier in the range of $$E_{0}=1$$ –100 PeV.