At zero field CsCuCl3 is known to form a helical spin structure along the c-axis and the 120-degrees structure in the c-plane. This paper discusses theoretically the effect of a magnetic field applied perpendicular to the c-axis, which breaks the axial symmetry. First the classical ground state is studied. The transverse magnetic field deforms the helical spin structure and causes a continuous phase transition from the helical (i.e. incommensurate) spin structure to a commensurate state, as the field increases. Detailed studies are made of the helix pitch and of the nature of the inconunensurate spin structure as functions of the field. The commensurate state has a nontrivial degeneracy, which is lifted by quantum (and thermal) fluctuations. Therefore the 1/S expansion is applied to determine the spin structure of the commensurate state. From these studies possible spin structures are suggested for each region of field strength.
