The purpose of this work is to study the structure and nature of the singul
arities of wavefronts in flat space-time. We computed the behavior at the s
ingularities of important objects that take place in the null surface formu
lation of general relativity. As a secondary result we show that the Minkow
ski space-time with non-trivial null surfaces is a solution of the null sur
face approach to general relativity.