  We address the problem of second order conformal deformation of spacelike
surfaces in compactified Minkowski 4-space. We explain the construction of the
exterior differential system of conformal deformations and discuss its general
and singular solutions. In particular, we show that isothermic surfaces are
singular solutions of the system, which implies that a generic second order
deformable surface is not isothermic. This differs from the situation in
3-dimensional conformal geometry, where isothermic surfaces coincide with
deformable surfaces.
