Absorption of radiofrequency (RF) waves within the Alfvén range of frequencies (Ω < ωHi) and current drive generation by Alfvén waves are studied in a cylindrical plasma column, with particle, heat and magnetic field diffusion processes taken into account. To this end, a 1-D numerical code describing RF field propagation, absorption and current drive processes has been developed, with a self-consistent evolution of the plasma parameters. The code structure includes electrodynamic and transport equations that are solved alternatingly with a 1 ms time order step. – Two different regimes have been found in the model, depending on the direction of the RF field rotation. Below the Alfvén threshold frequency, drift Alfvén mode pumping and RF field conversion into an ion acoustic wave have been found for a hollow current density distribution. It is shown that the helical (kink) resonance regime with wavenumbers m < 0 and n < 0 is the most promising for plasma heating. The efficiency of steady state current sustainment for the INTOR device parameters is of the order of 0.5 A·W−1.