An isotropic prestress theory for the Reynolds stress, developed recently by Parks et al. (1998), is extended to include an anisotropic component of the turbulent prestress correlation induced by pressure fluctuations and fluctuations in the instantaneous Reynolds stress. A turbulent Deborah number, Det = λγ, controls the long time response of the Reynolds stress subjected to a mean velocity gradient. A preclosure relaxation group, NR = τvγ, controls the short time response of the Reynolds stress. For simple shear flows, the phenomenological theory predicts the existence of nonzero primary and secondary normal stress differences.