The transcriptional repressor Hes1, a basic helix-loop-helix family protein, periodically changes its expression in the presomitic mesoderm. Its periodic pattern of expression is retained in a number of cultured murine cell lines. In this paper, we introduce an extended mathematical model for Hes1 oscillatory expression that includes regulation of Hes1 transcription by Drosophila Groucho (Gro) or its vertebrate counterpart, the transducine-like enhancer of split/Groucho-related gene product 1 (TLE1). Gro/TLE1 is a necessary corepressor required by a number of DNA-binding transcriptional repressors, including Hes1. Models of direct repression via Hes1 typically display an expression overshoot after transcription initiation which is not seen in the experimental data. However, numerical simulation and theoretical predictions of our model show that the cofactor Gro/TLE1 reduces the overshoot and is thus necessary for a rapid and finely tuned response of Hes1 to activation signals. Further, from detailed linear stability and numerical bifurcation analysis and simulations, we conclude that the cooperativity coefficient (h) for Hes1 self-repression should be large (i.e. h>or=4). Finally, we introduce the characteristic turnaround duration, and show that for our model the duration of the repression loop is between 40 and 60 min.