We extend the quasi-steady-state approximation (QSSA) with respect to the c
lass of differential systems as well as with respect to the order of approx
imation. We illustrate the first extension by an example which cannot be tr
eated in the frame of the classical approach. As an application of the seco
nd extension we prove that the trimolecular autocatalator can be approximat
ed by a fast bimolecular reaction system. Finally we describe a class of si
ngularly perturbed systems for which a higher order QSSA can easily be obta
ined.