The atmospheres of classical Cepheids cannot be represented adequately by a sequence of hydrostatic equilibrium atmospheric models (see Sasselov and Lester 1990 and references therein). Observational evidence for shocks is also available at least since Kraft (1956). Both the disequilibrium and the non-linear phenomena affect the emergent spectra and spectral line profiles of the Cepheids. In the lower amplitude variables the effects may be subtle, yet still lead to significant systematic discrepancies.

We have developed the code HERMES for time-dependent treatment of hydrodynamics and non-LTE radiative transfer in the atmospheres of classical Cepheids with periods shorter than 12 days. Our approach is applicable to stars in which the formed shock waves do not dominate the energy balance of the atmosphere. Consecutive detailed calculations are performed for several multi-level model atoms, including H, Ca II, Mg II, He I and II. We use a 1-D explicit conservative upwind monotonic second-order (in time and space) Godunov-type Lagrangian hydrodynamic scheme. Being a characteristics based scheme it allows natural handling of boundary conditions. The scheme is stable and without artificial dissipation, a crucial necessity for physically meaningful radiative transfer solutions (see Roe 1990, Sasselov and Raga 1991 for more details).