In this paper it is demonstrated that the Gauss’s principle also can be formulated in a parametric formulation of the mechanics of rheonomic systems, which is based on a family of varied paths, and on the transition to a new parameter, retaining the time as the independent variable. In this manner, one obtains the Gauss’s principle, both in a differential form and in the form of a principle of least constraint, including as well their presentation in generalized coordinates. From so formulated principle follows an extended system of corresponding Lagrange’s and Gibbs-Appell’s equations, and in all so obtained relations appears one additional term or equation, arising from the nonstationarity of constraints, which is characteristic for this parametric formulation of mechanics.