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Cosmogenic radionuclides with half-life periods T1/2 ranging from several days to a million years, produced in the nuclear reactions of galactic cosmic rays (GCR) with meteoritic matter, provide valuable information on the GCR intensity variations on a long time scale (∼1 million years) within meteorite orbits 2–4 AU from the Sun. Information on the variations of GCR gradients in the inner heliosphere was obtained by comparing the measured contents of 54Mn and 22Na in stone meteorites (chondrites) with known orbits at the time of their fall to Earth with the calculated production rates of these radionuclides in them using balloon intensity measurements of GCR (E > 100 MeV) in the stratosphere at appropriate times. Although individual gradient values show significant uncertainties, the important information is that cosmogenic radionuclides in chondrites predict low gradients (0–10% per 1 AU) for all periods of minimum solar activity in 1957–2013, according to direct measurements in interplanetary space. High gradients (50–100% per 1 AU) are predicted for periods of maximum solar activity, especially in 1992 and 2012 (up to ∼200% per 1 AU). Average values of gradients are (20 ± 10)% per 1 AU for modern solar cycles (according to the production rate of 22Na), similar to the average values for the last ∼1 million years (according to the production rate of 26Al), which indicates the constancy of the solar modulation of the GCR, at least for the last million years.