The behaviour of composite frame - shear wall systems with regard to creep and shrinkage with high beam stiffness has been largely unattended until recently since no procedure has been available. Recently an accurate procedure, termed the Consistent Procedure (CP), has been developed which is applicable for low as well as for high beam stiffness. In this paper, CP is adapted for a class of composite frame - shear wall systems comprising of steel columns and R.C. shear walls. Studies are reported for the composite systems with high as well as low beam stiffness. It is shown that considerable load redistribution occurs between the R.C. shear wall and the steel columns and additional moments occur in beams. The magnitude of the load redistribution and the additional moment in the beams depend on the stiffness of the beams. It is also shown that the effect of creep and shrinkage are greater for the composite frame - shear wall system than for the equivalent R.C. frame - shear wall system.