How far one can go with the Exp-function method?

A criterion determining if an exact solution of a differential equation can be expressed in a form comprising a finite number of exponential functions is constructed in this paper. This criterion is based on the concept of ranks of Hankel matrixes constructed from sequences of coefficients produced by symbolic multiplicative operator techniques. The employment of this criterion also gives an answer on the structure of the solution. Several examples are used to illustrate this concept.