Abstract <p>The observed power-law spectra of relativistic jets from active galactic nuclei clearly indicate a synchrotron mechanism of radiation by particles that similarly possess a power-law energy spectrum. However, the issue of their angular anisotropy has not been given sufficient attention until recently, although the example of the solar wind (where a strongly magnetized wind is realized in a similar way) shows the importance of taking this circumstance into account. In this paper, we study the evolution of an initially isotropic power-law spectrum of radiating particles as they propagate along expanding relativistic jets. It is shown that for relativistic flows in which the electric field plays a crucial role, the preservation of the first adiabatic invariant does not lead to a decrease in the pitch angles of radiating particles as they enter the region of weak magnetic fields. This is due to the drift nature of the particle motion.</p>