This paper presents a general procedure for including added effects, such as turbulent dissipation rate anisotropies, into algebraic stress formulations in both inertial and noninertial frames of reference. Explicit algebraic stress models, which assume an isotropic turbulent dissipation rate, have been developed previously and extended for application to noninertial frames. Independently, anisotropic dissipation rate models have also been developed. Recently, an algebraic, anisotropic dissipation rate model has been developed and used in conjunction with a full Reynolds stress closure. Unfortunately, in the theoretical formulations used previously for explicit algebraic models, the combination of the algebraic stress and algebraic dissipation rate models only appeared possible for inertial frames. The alternative procedure outlined here remedies this problem and allows for the construction of a composite model for both inertial and noninertial frames. This new composite model formulation is tested in homogeneous shear with and without rotation, and in strongly rotating channel and pipe flows using different types of anisotropic dissipation rate models. ©1998 American Institute of Physics.