[en] The authors consider resonance at the harmonics of the electron cyclotron frequency in a magnetic field whose value has an extremum. A calculation is given of the electromagnetic-wave absorption coefficients at electron cyclotron resonance with allowance for different broadening mechanisms for the second and higher harmonics. It is shown that the wave absorption at resonance near the magnetic field extrema is determined by the nature of the absorption line broadening, whereas the absorption coefficient sufficiently far from the extrema is independent of the broadening mechanism and can be defined by a single analytical expression. The possibility of using the results for making local measurements of the plasma density, the electron distribution function and the magnetic field strength in adiabatic traps is discussed. (author)