  On the basis of recent work by Cardin and Teixeira on ordinary differential
equations with more than two time scales, we devise a coordinate-independent
reduction for systems with three time scales; thus no a priori separation of
variables into fast, slow etc. is required. Moreover we consider arbitrary
parameter dependent systems and extend earlier work on Tikhonov-Fenichel
parameter values -- i.e. parameter values from which singularly perturbed
systems emanate upon small perturbations -- to the three time-scale setting. We
apply our results to two standard systems from biochemistry.
