We investigate the stabilizing effects of a constant horizontal magnetic field on the flow in a heated planar liquid metal layer. The magnetic field is either transverse or longitudinal with respect to the imposed temperature gradient driving the buoyant shear flow. Two main instabilities are triggered in such flows: stationary transverse instabilities and oscillatory longitudinal instabilities. Each magnetic field is unable to stabilize the instabilities which develop in a plane perpendicular to its direction, so that the transverse field only affects the longitudinal instabilities and the longitudinal field the transverse instabilities. The results obtained by an approximate analytical linear stability analysis reveal a similar behaviour in both cases: small variation of the thresholds (critical Grashof number, Gr(c)) and of the wavelengths at small Ha (Ha is the Hartmann number proportional to the intensity of the magnetic field) before an increase leading to asymptotic linear variations at large Ha. Comparisons with the results obtained in the case of a vertical magnetic field [S. Kaddeche et al., J. Crystal Growth, Part 1] show that the horizontal fields generate less efficient stabilizing effects. (C) 2002 Elsevier Science B.V. All rights reserved.