A multivariate generalization for line integrals of the Strong Liouville Theorem due to Risch is presented. The result is an abstract version of the following: Let k be a subfield of the field of complex numbers. Let each, be any function in a field E obtained by algebraic operations and the taking of logarithms and exponentials over. If there exists a functions g obtained by algebraic operations and the taking of logarithms and exponentials of elements of E such thatthen g must be of the formwhere dois in E, the ciare constants in k(a), and the diare elements in E(a), where a is a constant algebraic over E.