On global transformations of functional-differential equations of the first order

The paper describes the general form of functional-differential equations of the first order with m(m greater than or equal to 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),...,v(m))u+h(t,x,u,u(1),...,u(m))v for u not equal 0 is solved on R and a method of proof by J. Aczel is applied.