Boundary layer transition induced by high levels of free stream turbulence (FSl), so called bypass transition, can not be predicted with conventional stability calculations (e.g. the en-method). The use of turbulence models for transition prediction has shown some success for this type of flows, and the present study is a further investigation on the use of low-Reynolds number, single-point closures for transition prediction. The work is focused on two differential Reynolds Stress Models (DSM), which are compared with the in previous studies more elaborately tested two-equation model by Launder Sharma. The results obtained with the DSM are relatively promising in some test cases, with a qualitatively correct description of the different normal stresses throughout the computational domain. However, the applicability of the models is very limited if a wider range of test cases are considered. Although the Differential Reynolds Stress Models have better prospects to describe the very anisotropic fluctuations that are observed in transitional boundary layers, the overall predictions of the location of the transition region are worse than obtained with the two-equation model. Detailed comparisons with results from Large Eddy Simulations have revealed significant shortcomings in the modelling of the dissipation. The DSM suffer from a large overprediction of the dissipation in the pre-transitional boundary layer, which also affects the modelling of the pressure strain terms. The present study also shows that some of the results reported in the literature may be too optimistic, since they seem to be affected by the implementation of the free stream boundary conditions. The predictions are sensitive to the FST-level in the vicinity of the boundary layer edge, and large variations in the predicted transition location can be obtained depending on how the free stream boundary is treated. The outcome of the present study indicates that, if single-point closures are going to be considered as a realistic transition prediction tool for industrial applications, some major improvements in the modelling are necessary.