The cosmic ray fluxes in four consecutive solar activity minima (1964--1965, 1976--1977, 1987, and 1996--1997) are considered. The data obtained in long-term stratospheric measurements and at ground level (neutron monitor and ionization chamber data) are used. The long-term negative trend is derived from these experimental data. The value of the effect is Δ≈-(0.01--0.09)% per year. The data on cosmogenic radioactive isotopes of 10Be and 14C which are produced by cosmic rays in the atmosphere also show the gradual decrease of their concentrations on the timescale of more than ~104 years. The stratospheric measurements also propose that the cosmic ray spectrum becomes softer in the energy range E=0.1--1.5 GeV with the passage of time. The consideration of solar and interplanetary parameter changes, which could be responsible for the observed negative trend in cosmic ray flux, does not show any increase. The effect could be explained if supernova explosion had taken place in the nearby interstellar space. Such an explosion could occur about 104-5¿105 years ago at the distance 30--150 pc from the solar system. ¿ 2000 American Geophysical Union