Context. In the recent years, infrared interferometry revealed the presence of faint dusty circumstellar envelopes (CSE) around Cepheids. However the size, shape, chemical nature, and the interaction of the CSE with the star itself are still under investigation. The presence of a CSE might have an effect on the angular diameter estimates used in the interferometric Baade-Wesselink and surface-brightness methods of determining the distance of Cepheids. Aims. By studying Hα profiles as a function of the period, we investigate the permanent mass loss and the CSE around Cepheids. Our high spectral- and time-resolution data, combined with a very good S/N will be useful to constrain future hydrodynamical models of Cepheids’ atmosphere and their close environment. Methods. We present HARPS ⋆⋆ high resolution spectroscopy (R = 120000) of eight galactic Cepheids : R Tra, S Cru, Y Sgr, β Dor, ζ Gem, RZ Vel, l Car and RS Pup, providing a good period sampling (P = 3.39d to P = 41.52 d). The Hα line profiles are described for all stars using a two-dimensional (wavelength versus pulsation phase) representation. For each star, an average spectral line profile is derived, together with its first moment (γ-velocity) and its asymmetry (γ-asymmetry). Results. Short-period Cepheids show Hα line profiles following the pulsating envelope of the star, while long-period Cepheids show very complex line profiles and, in particular, large asymmetries. We find a new relationship between the period of Cepheids and their γ-velocities and -asymmetries. These results may be related to the dynamical structure of the atmosphere and to a permanent mass loss of Cepheids. In particular, we confirm for l Car a dominant absorption component whose velocity is constant and nearly of zero km s 1 in the stellar rest frame. This component is attributed to the presence of circumstellar envelope. Conclusions. To understand these very subtle γ effects, fully consistent hydrodynamical models, including pulsating and evolutionary theories, convective energy transport, adaptive numerical meshes, and a refined calculation of the radiative transfer are required.