Static and dynamic properties of complexes formed by hyperbranched polymers with linear polyelectrolytes are studied under the influence of steady shear flow by means of Brownian dynamics simulations. Models of peripherally charged hyperbranched molecules bearing two extreme topological structures and different molecular weights complexed with linear neutralizing chains are subjected to a range of shear rates starting from a low-shear regime toward the complex-breaking point. Examination of the stability limit, shape and mass distribution parameters, and dynamics in different lengths and timescales is performed as a function of the applied shear. The results described illustrate features of the generic behavior that should be expected from such systems under conditions of steady shear flow.