Drawing from the results of theoretical studies about the behaviour of constant-coefficients semi-implicit schemes, the dynamical kernel of the Aladin–NH spectral limited-area numerical weather prediction (NWP) model has been modified in order to allow for a stable and efficient integration of the fully elastic Euler equations. The resulting dynamical kernel offers the possibility to use semi-Lagrangian transport schemes together with two-time-level discretizations at kilometric scales for NWP purposes. The main characteristics of the adiabatic part of the model formulation and the space and time discretization are described in this article. In order to illustrate the dependence of the results on adjustable parameters of the dynamical kernel, some real-case dynamical-adaptation forecasts performed with a basic physical parameterization package are presented. The results obtained with this model in real-case experiments fully confirm the conclusions drawn in previous numerical analysis studies. The good quality of the results is found to be compatible with a routine exploitation in a NWP framework. The Aladin–NH dynamical kernel has been used in the operational NWP ‘AROME’ model since December 2008 at the kilometric scale, with an appropriate physical parameterization package and data assimilation system. Copyright © 2010 Royal Meteorological Society and Crown Copyright.