  We introduce null surfaces (or nullcone fronts) of pseudo-spherical spacelike
framed curves in the three-dimensional anti-de Sitter space. These surfaces are
formed by the light rays emitted from points on anti-de Sitter spacelike framed
curves. We then classify singularities of the nullcone front of a
pseudo-spherical spacelike framed curve and show how these singularities are
related to the singularities of the associated framed curve. We also define a
family of functions called the Anti-de Sitter distance-squared functions to
explain the nullcone front of a pseudo-spherical spacelike framed curve as a
wavefront from the viewpoint of the Legendrian singularity theory. We finally
provide some examples to illustrate the results of this paper.
