The reliable prediction of turbulent non-equilibrium flows is of high academic and industrial interest in several engineering fields. Most turbulent flows are often predicted using single-time-scale Reynolds-Averaged-Navier-Stokes (RANS) turbulence models which assume the flows can be modelled through a single time or length scale which is an admittedly incorrect assumption. Therefore they are not expected to capture the lag in the response of the turbulence in non-equilibrium flows. In attempts to improve prediction of these flows, by taking into consideration some features of the turbulent kinetic energy spectrum, the multiple-time-scale models arose. A number of two-scale models have been proposed, but so far their use has been rather limited.This work thus focusses on the development of two-time-scale approaches. Two two-time-scale linear-eddy-viscosity models, referred to as NT1 and NT2 models, have been developed and the initial stages of the development of two-time-scale non-linear-eddy-viscosity models are also reported. The models' coefficients have been determined through asymptotic analysis of decaying grid turbulence, homogeneous shear flows and the flow in a boundary layer in local equilibrium. Three other important features of these models are that there is consistent partition of the large and the small scales for all above limiting cases, model sensitivity to the partition and production rate ratios and sensitivity of the eddy viscosity sensitive to the mean strain rates.The models developed have been tested through computations of a wide range of flows such as homogeneous shear and normally strained flows, fully developed channel flows, zero-pressure-gradient, adverse-pressure-gradient, favourable-pressure-gradient and oscillatory boundary layer flows, fully developed oscillatory and ramp up pipe flows and steady and pulsated backward-facing-step flows.The proposed NT1 and NT2 two-scale models have been shown to perform well in all test cases, being, among the benchmarked models tested, the models which best performed in the wide range of dimensionless shear values of homogeneous shear flows, the only linear-eddy-viscosity models which predicted well the turbulent kinetic energy in the normally strained cases and the only models which showed satisfactory sensitivity in predicting correctly the reattachment point in the unsteady backward facing step cases with different forcing frequencies. Although the development of the two-time-scale non-linear-eddy-viscosity models is still in progress, the interim versions proposed here have resulted in predictions of the Reynolds normal stresses similar to those of much more complex models in all test cases studied and in predictions of the turbulent kinetic energy in normally strained flows which are better than those of the other models tested in this study.