  We demonstrate how to find modular discrete symmetry groups for $Z_N$
orbifolds. The $Z_7$ orbifold is treated in detail as a non-trivial example of
a $(2,2)$ orbifold model. We give the generators of the modular group for this
case which, surprisingly, does not contain $\sltz^3$ as had been speculated.
The treatment models with discrete Wilson lines is also discussed. We consider
examples which demonstrate that discrete Wilson lines affect the modular group
in a non-trivial manner. In particular, we show that it is possible for a
Wilson line to break $SL(2,{\bf Z})$.
