In CsFeCl3 the Fe2+-ion with effective spin one has locally a singlet ground state (m s =0). The ferromagnetic interactions along thec-direction and the anti-ferromagnetic interactions perpendicular to it are too week as compared to the anisotropy to introduce longrange order in the absence of an external field. By inelastic neutron scattering we have investigated the excitation spectrum in an external magnetic field up to 6 T applied perpendicular to thec-axis. Preliminary measurements in zero field show that dipolar effects lead to a shift of the minimum of the dispersion curve away from theK-point. We show that with increasing magnetic field the whole dispersion sheet is shifted towards higher frequencies and a splitting appears. With the help of a local Hamiltonian which neglects exchange interactions between all neighbours we give a qualitative explanation of the intensity of the magnetic excitations in dependence of the magnetic field. A more sophisticated theory (RPA-diagonalisation of the Heisenberg-Hamiltonian that is used to describe the magnetic behaviour of CsFeCl3) yields — apart from a mismatch for the modes at high energy transfers — a satisfactory description of the magnetic excitations of CsFeCl3 in dependence of the magnetic field.