The evolutions of the mid-latitude cosmic ray (CR) neutron monitor intensities and interplanetary and solar indices for 1996–2003 (rising phase of solar cycle 23) showed the following: (1) Monthly values: Most of the solar indices started increasing by July 1997 and reached a first peak near July 2000, a second peak near October 2001, and a third minor peak near September 2002. However, CR remained at an almost steady level up to March 1998, suffered a sharp decline during March–May 1998, remained almost steady up to July 1999, decreased thereafter almost smoothly up to July 2000 (first trough), and fluctuated thereafter to have a second trough in September 2002. The solar open magnetic flux (<45° solar latitude) and IMF B component did not change fully parallel to the solar indices. (2) Daily values: CR depressions mostly coincided well with geomagnetic Dst, but sometimes, the two were dissimilar. Also, CR and many other parameters showed oscillations with peak spacings of 7–27 days. (3) Hourly values: cosmic rays showed (Forbush) decreases evolving in a very similar way to geomagnetic Dst, particularly when the IMF B was large. We do not think that the idea that the long-term modulation in step-like form is caused by the propagating diffusive barriers “Global” MIRs (GMIRs) (e.g., Burlaga, L.F., McDonald, F.B., Ness, N.F., 1993. CR modulation and the distant heliospheric magnetic field: Voyager 1 and 2 observations from 1986 to 1989, near 11 AU. J. Geophys. Res. 98, 1–11) and the alternative suggestion (e. g., Cane, H.V., Wibberenz, G., Richardson, I.G., von Rosenvinge, T.T., 1999. CR modulation and the solar magnetic field. Geophys. Res. Lett. 26, 565–568) that the step-like changes (medium-term events, lasting about an year) were related to a fundamental process at the Sun, are mutually exclusive. Both the processes are operative simultaneously, only that the relationship with near-Earth IMF is more spectacular as it occurs with considerable CR changes in a short time (hours to few days). During the absence of near-Earth events, the effects of GMIRs are seen clearly as slow CR decreases lasting for several days.