From an analysis of the time variations during 1968-1971 of the fast neutron flux in the upper atmosphere (mean energy of response to primaries, 1-2 GeV per nucleon) versus those of ground-based neutron monitors we have identified two classes of transient intensity decrease on the basis of differences in their spectral responses, time histories, and flare associations. Type I events are found to be classic Forbush decreases, sharp declines accompanying a geomagnetic storm sudden commencement, following by 1-3 days a large optical flare with radio noise and energetic particle production, whereas type II events are more symmetric in their time histories and are therefore not associated with a particular flare. There are also differences in the spectral responses of the two types. During a type I decrease the flux change of the lower-rigidity cosmic ray particles lags the flux change of the high-rigidity particles both in the decline and in the recovery, tracing out a hysteresis loop. During a type II event, if there is any hysteresis at all, the lower-rigidity primaries tend to 'overrecover' in comparison to the higher-rigidity primaries. Intercomparison of neutron monitor data for median response rigidities from 10 to 30 GV reveals that the spectral response in type II events is softer on the average for low-rigidity (10 GV) primaries than that in type I events. Comparison of intermixed sequences of type I and II events with recurrences of active regions reveals an identifiable but complex evolutionary relation between decrease occurrence and active region development. Long-lived (of the order of days) low-energy (<1 MeV) proton events occur during all but one of the type II events identified, supporting an association with solar active region transits. We interpret type II events as either a subsequent evolution of type I (Forbush decrease) events or a quasi-stationary 'corotating' spatial structure loosely associated with an active region. Therefore both type I and type II decreases occur in intermixed recurrence series at intervals of 20-30 days.