The amount of compound words in ancient Greek makes its hyphenation by computer a quite difficult task; it is impossible to predict all combinations of words. To be efficient, a set of patterns must be accessible to the final user; a scholar must be able to add patterns, according to new words he/she encounters. Use of TeX's \hyphenation primitive is not appropriate since most Greek words are declinable: for each word one would have to add a dozen hyphenation exceptions. After a short introduction to the concept of hyphenation by TeX the author presents a method for hyphenation of ancient Greek. Using this method. he compiled a list of patterns out of the Bailly 50,000-word dictionary. These patterns are presented in a comprehensible format, in a way that scholars can easily determine the patterns that have to be added, to solve specific hyphenation problems. The same approach is applied to Latin. A list of patterns has been compiled out of a dictionary (Bornecque and Cauët). The size of this list is very small compared to the one of ancient Greek patterns. although Latin also uses compound words. Finally examples of hyphenated classical texts are given.