The increasing level of solar activity at the end of 1997 coincides with the observation of solar energetic particle (SEP) events by the Wind and Ulysses spacecraft. The proximity of Ulysses to the ecliptic plane during this period allows us to study the effects of the solar activity at two different heliolongitudinal and heliocentric distances but at similar heliolatitudes. We identify the main transient proton enhancements seen by Wind and Ulysses from October 1997 to the end of December 1998. We compare their characteristics and suggest an interpretation in terms of their heliospheric location, the activity occurring at the Sun, and the conditions for particle propagation between the Sun and both spacecraft. Whereas at 1 AU different SEP events can be associated with individual coronal mass ejections (CMEs), at 5 AU long-lasting SEP events are observed while a sequence of CMEs takes place at the Sun. Continuous injection of particles from traveling CME-driven shocks, the effects of particle propagation along interplanetary magnetic field lines, and the corotation of these field lines across the Ulysses location are the main factors responsible for these long-lasting periods of high particle intensity observed by Ulysses. ¿ 2000 American Geophysical Union