From 1957 to 1960, Kochelaev was a post-graduate student of the Experimental and Theoretical Physics Department of Kazan University under the supervision of Semen Altshuler.

From 1968 until now, Boris Kochelaev has been a professor, and from 1973 to 2000, he was chair of Kazan University's Theoretical Physics Department.

33 PhD-level scientists were supervised by Kochelaev, 10 of them have obtained doctoral degrees and become full professors.

The research interests are focused on electron spin resonance and spin dynamics in condensed matter, superconductivity, propagation of sound in resonant media, and light scattering in solids.

Major research achievements: These last theoretical investigations are best described by Nobel Prize winner Prof. K. Alex Müller in the paper titled "The Impact of ESR (EPR) on the Understanding of Cuprates and Their Superconductivity": this important advance was achieved by the experimental results at the universities of Darmstadt and Zürich on the one side and the deep theoretical insight of Boris Kochelaev at the Kazan State University explaining them on the other side.