Time-series of Hα spectra with relatively high resolution in wavelength (R = lambda /delta lambda of 15 000 to 22 000) and time (Delta t = 1d) of the late-type O supergiant alpha Cam are analysed in terms of line-profile variability (lpv). The spectra cover an interval of one year, from February 1998 to February 1999. The analysis provides clear evidence of a continuous deep-seated wind activity traced by variations in the Hα emission and He I lambda 6678.15 absorption lines. The observations indicate that the wind is not smooth but perturbed, starting from its base up to velocities of ~ 500 km s-1. The character of the medium-term (days) variations found in Hα changes between epochs, and appears to require an explanation involving different kinds of wind perturbations. In particular, we found that in June and July 1998 as well as in February 1999 the lpv of Hα was dominated by low-amplitude (<=+/-10%) variations in line flux which usually occupy the central part of the profile symmetrically with respect to the line center while in December 1998 and January 1999 the variations were organised in two wave-like modulations that run from ``red'' to ``blue" and back to ``red" within the profile (between +/-300 km s-1), being most of the time in antiphase. The timescale of variation, revealed via Fourier analysis, is respectively ~ 7 and ~ 10 days. Significant variations in emission equivalent width (up to 35%), closely linked to those in the line profile, are also noted. Short-term (3 to 4 days), low-amplitude (<=22%) variation in mass loss rate which recurs on a timescale of ~ 7 days giving rise to the formation of outward accelerating consecutive shells or/and blobs was suggested to explain the lpv of Hα in June-July 1998 and in February 1999. Whereas the variability pattern observed in December-January 1999 seems to be qualitatively consistent with a model involving two rotationally-modulated wind perturbations, one of enhanced density and another of reduced density with respect to the mean, which are not symmetric about the center of the star. Strange-mode oscillations or radial fundamental pulsation are discussed as possible mechanisms generating the established wind variability.