The authors report on synchrotron X-ray studies of the nematic (N) and the smectic-A (SMA) phases under nonequilibrium 'steady state' shear flow conditions. Under shear, the presence of SMA fluctuations leads to a novel flow-induced fluctuation force on the nematic director n which alters its equation of motion. This leads to rich behaviour where the nematic phase exhibits a sequence of regimes in which the orientational phase space (OPS) explored by n evolves as the N-SMA transition is approached. They directly observe the critical slowing down of the SMA order parameter fluctuations through the X-ray profiles which give the intensity map of the time- and space-averaged OPS traversed by n. The data are consistent with the classical Ericksen-Leslie-Parodi theory of nematodynamics away from the immediate vicinity of the N-SMA transition temperature. Closer in, however, fluctuation effects dominate and a model of critical nematodynamics has to be considered. The experiments demonstrate that synchrotron scattering techniques may be used as effective structural probes of dynamical systems.