  We determine the Lagrangian monodromy group L(T) and the smooth monodromy
group S(T) of a Clifford torus T in the symplectic 4-space. We show that L(T)
is isomorphic to the infinite dihedral group, and S(T) is generated by three
reflections. We give explicit formulas for both groups. We also show that if a
Lagrangian torus is smoothly isotopic to a Clifford torus then the smooth
isotopy can be chosen to be Lagrangian outside of a disc.
