Effect of external magnetic field on the screw structure of spin arrangement at absolute zero is studied in detail for the case where the field is applied perpendicularly to the screw axis. First, the anisotropy energy which confines the spin vectors in the plane perpendicular to the screw axis is assumed to be so large that for any strength of the field the spin vectors remain in that plane. For weak fields, the change of the screw structure due to the field is calculated as a power series of the field strength and the calculation of the energy of the system is carried out up to the fourth power. A singularity appears for turn angles of 90° and 180°. For high fields, expansion in powers of the deviation angles of the spin vectors from the field direction is made, and it is shown that there is a critical field, H0, above which the vectors are all parallel to the field direction and below which they oscillate sinusoidally about the field direction with an amplitude which is proportional to (H-H0)1/2. Phase transition between the screwing and sinusoidally oscillating structures at an intermediate field strength is discussed. In the neighbourhood of turn angles of 90°, 180°, and 60°, there appear regions of stability of doubly antiferromagnetic, antiferromagnetic, and triangular arrangements. Second, the assumption for the anisotropy energy is relaxed, and phase transitions between the screwing, cycloidal (more strictly, elliptically conical), and sinusoidally oscillating structures are studied for small turn angles.