The medium-entropy alloy (NbTa)(0.67)(HfZr)(0.33 )and the high-entropy alloy (NbTa)(0.67)(HfZrTi)(0.33) were prepared by mechanical alloying using high-energy planetary ball mill. The results of X-ray diffraction, scanning electron microscopy, and positron annihilation lifetime spectroscopy measurements suggest that both as-prepared powders are multicomponent alloys in amorphous (or highly disordered) state. The magnetic and thermodynamic results obtained for these powders undoubtedly prove that bulk superconductivity is not observed at temperatures exceeding 2 K. Thermal treatment of both studied materials leads to decomposition of the amorphous phase and precipitation of several crystalline phases. In both annealed samples, the structure of the main crystalline phase was identified as body-centered cubic (bcc), and in this phase, bulk superconductivity was observed below 6.5 K.