It is analyzed a mechanically compensated zoom lens in which the second and fourth components are movable to attain zooming effects, while the first, third and fifth components are fixed during zooming. It is derived a set of quartic and two (or four) elements simultaneous zoom equations each of which simultaneously satisfies two paraxial conditions; continuous change of magnification (or focal length) and constant object-image distance. Analytical solutions are obtained together with an approximate zoom equation in the vicinity of a critical point and that near a singular point. Numerical example is added to show the effectiveness of the analysis.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.