The Be star HR 2501 was monitored in photometry, from 1978 to 1998 in the GENEVA system and from 1990 to 1992 by the HIPPARCOS satellite, and in spectroscopy from 1998 to 2001 by using the CORALIE spectrograph. Several mostly unrelated periods or time scales characterize the variability of HR 2501. First, the radial velocity data reveals that this is a new lambda Eri star, with a period of 0.79187 d due to non-radial pulsations or clouds close to the stellar photosphere. Second, both GENEVA and HIPPARCOS photometries exhibit a mid- to long-term variability of characteristic time similar to500 d and peak-to-peak amplitude similar to0.4 mag, most probably a consequence of the recurrent outbursts of matter from the rapidly rotating Be star towards its disk. Third, a characteristic time of similar to300 d between the outbursts is shown by spectroscopy by looking at the variations of the equivalent width of Halpha, Hbeta and Hel (5875.6 Angstrom) emission lines (the outbursts studied in photometry and spectroscopy are unfortunately not the same due to the non-simultaneity of the monitorings). Fourth, the VIR ratio of the double peaks in Ha and H,8 show a periodic-type variation during the second of the spectroscopic outbursts, with periods of respectively 16.7 and 15.1 d, in agreement with the prediction of the dynamical evolution of a blob of material ejected from the equator of the star into the Keplerian disk. Fifth, a short-term photometric period of 0.46 d is detected during an epoch of intensive monitoring; however, it must be noted that if this variability is confirmed, the value of this short-term period is unsure. The other main results are: i) During the 27 months of the spectroscopic survey, in addition to the mentioned outbursts, the emission in Ha and H,8 lines decreased progressively until it almost completely vanishes at the end. ii) The estimated radius of the circumstellar disk varies and reaches 5.5, 4 and 2 stellar radii at maximum for the Ha, H,8 and Hel emission regions respectively; iii) The spectroscopic monitoring was particularly successful, and the series of observation of the line profiles, with the variation of the emission from day to day, is quite exceptional in the studies of Be stars.