The paper describes the general form of functional-differential equations of the first order with $m(m\ge 1)$ delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation $$f(t,uv,u_1{v}_1,...,u_m{v}_m)=f(x,v,v_1,...,v_m)g(t,x,u,u_1,...,u_m)u+h(t,x,u,u_1,...,u_m)v$$ for $u\ne 0$ is solved on $ℝ$ and a method of proof by J. Aczél is applied.

The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form $$f(t,vy,wy+uvz)=f(x,y,z)u^{2}v+g(t,x,u,v,w)vz+h(t,x,u,v,w)y+2uwz$$ is solved on $ℝ$ for $y\ne 0$, $v\ne 0.$