The author studies the system of equations \[ F_k(x,u,p,\phi) = 0,\quad k=1,2,\dots,s\tag{1} \] with an arbitrary element \(\,\phi=(\phi^1,\dots,\phi^r)\), where \(\,x=(x_1,\dots,x_n)\in \mathbb R^n\,\) are independents variables, \(\,u=(u^1,\dots,u^m)\in \mathbb R^m\,\) are dependents variables, \(p\) are derivatives of dependents variables \(u\) with respect to independent \(x\) until some order \(r\). Basing on general results the author proposes generalized equivalence transformations of system (1).