A styrene copolymer with methacrylic acid containing less than 5 mol % of spin-labeled methacrylic acid chain units distributed randomly along the polymer main chain (SL-ST-MA) was synthesized. ESR spectra of the copolymer were measured at X-band (9 GHz) in dilute solutions (ca. 1 wt %) over a broad temperature range in four solvents differing in thermodynamic quality, viscosity, and activation energy of viscous flow. Temperature dependences of the parameter R-S characterizing local dynamics in polystyrene chains and of other parameters characterizing dynamics in the copolymer were determined by fitting experimental ESR spectra to the MOMD model. Unlike so far published conclusions, the data show that the copolymer in the solvents used-Theta solvent dioctyl phthalate (DOP), marginal solvent dibutyl phthalate (DBP), and good solvents toluene (TOL) and dimethylformamide (DMF)-exhibits non-Kramers behavior characterized by the parameter alpha = 0.73 +/- 0.02 and by the height of the potential barrier for local conformational transitions E-a = 10.5 +/- 0.6 kJ/mol.