The time behavior of intensity of cosmic rays with relatively low (~1–6 GeV) and high (>10 GeV) energies are considered together with characteristics influencing the modulation of cosmic rays in the heliosphere. The periods under study are close to solar activity minima in cycles 21/22, 22/23, and 23/24. Diffusion and convection in small-scale magnetic fields of the heliosphere are demonstrated to play some role only at sufficiently weak disturbances of the field (B/δB > 1.3). In this case, a negative correlation is observed between B/δB and a tilt of the surface of the heliospheric current sheet. The analysis of characteristics of the interplanetary medium in periods of solar activity minima shows that the energy anomaly of cosmic rays in the minimum of cycles 23/24 is caused by deficit of high energy particles rather than by an excess of particles of relatively small energies.