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Context. Despite recent time series of very high quality of Ho- profile variations of classical Cepheids, the dynamics of the pulsating atmosphere of long-period Cepheids is not yet understood. Aims. Taking into account the propagation of intense shock waves in the atmosphere, we propose a general scheme of the atmospheric dynamics in long-period Cepheids. Methods. We use a time series of H alpha profiles of the long-period Cepheid X Cygni and HARPS high-resolution spectroscopy of three long-period Cepheids that have not yet been fully interpreted. Results. Caused by the main shock occurring at each pulsation cycle, the H alpha profile first presents a blueshifted component in emission or in absorption depending on the shock intensity. Then, when the shock is detached from the photosphere, the emission shifts on the red side of the line profile which now has the form of a P Cygni profile. A second shock is also observed. It is the consequence of the ballistic motion of the atmosphere. Thus, the interaction of the main shock with infalling layers can qualitatively explain observed variable peculiairities in the H alpha profile. Conclusions. The evolution of the H alpha profile occurring in long-period Cepheids is similar to the evolution observed in radially pulsating stars such as RR Lyrae stars, in which the intensity of the main shock is strong enough to induce a propagation away from the photosphere.