  Solutions of the wave equation in a space-time containing a thin cosmic
string are examined in the context of non-linear generalised functions.
Existence and uniqueness of solutions to the wave equation in the Colombeau
algebra G is established for a conical space-time and this solution is shown to
be associated to a distributional solution. A concept of generalised
hyperbolicity, based on test fields, can be defined for such singular
space-times and it is shown that a conical space-time is G-hyperbolic.
