  We present three dimensional smoothed particle hydrodynamics (SPH)
calculations of warped accretion discs in X-ray binary systems. Geometrically
thin, optically thick accretion discs are illuminated by a central radiation
source. This illumination exerts a non-axisymmetric radiation pressure on the
surface of the disc resulting in a torque that acts on the disc to induce a
twist or warp. Initially planar discs are unstable to warping driven by the
radiation torque and in general the warps also precess in a retrograde
direction relative to the orbital flow. We simulate a number of X-ray binary
systems which have different mass ratios using a number of different
luminosities for each. Radiation-driven warping occurs for all systems
simulated. For mass ratios q ~ 0.1 a moderate warp occurs in the inner disc
while the outer disc remains in the orbital plane (c.f. X 1916-053). For less
extreme mass ratios the entire disc tilts out of the orbital plane (c.f. Her
X-1). For discs that are tilted out of the orbital plane in which the outer
edge material of the disc is precessing in a prograde direction we obtain both
positive and negative superhumps simultaneously in the dissipation light curve
(c.f. V603 Aql).
