This article presents the results of research carried out on an experimental rolling mill with axial, cyclic movement of rolls (RCMR). The device was made on the basis of an unconventional technical solution for the movement of shaping tools and equipped with a complete measuring system recording all the parameters of the process. The research was conducted on selected copper alloys CuFe2 and CuCr0.6. Rolling tests in the RCMR process were carried out for rolling speeds vr = 3.1 × 10−3, 6.3 × 10−3and 9.4 × 10−3m/s, which correspond to the rotational speed of the rollers at ω = 1, 2 and 3 rpm for an active diameter of the rollers = 60 mm. In testing the thermal effects of the process, the rolling speed ω = 0.7 rpm was also used. A constant value of the frequency of axial movement of the rollers f = 1 Hz and the amplitude of the displacement of the rollers A = 0.8 mm were assumed. The rolling process for the strands was carried out in six culverts using the average relative crush in the passage of Δh = 15%. Conventional rolling tests were carried out to compare rolling processes, and the obtained data formed the basis for assessing the strain intensity and identifying local deformation zones in the RCMR rolling process. The waveforms of rolling pressures, intensity and non-uniformity of deformation, and increase in the temperature of the strip surface in subsequent culverts were compared with the results obtained in the conventional rolling process.