We consider the effect of real spectral singularities on the long time behavior of the solutions of the focusing Nonlinear Schrödinger equation. We find that for each spectral singularity λ ′ ∈ R, such effect is limited to the region of the (x,t)plane in which λ ′ is close to the point of stationary phase λ 0 = −x 4t (the phase here being defined in a standard way by, say, the evolution of the Jost functions). As we approach that region, the solution performs decaying oscillations; the order of decay is O((logt t) 1/2). Inside that region the solution is asymptotically identified as a selfsimilar solution of NLS expressible in terms of a Painlevé 4 transcedent. We prove our result by using the Riemann-Hilbert factorization formulation of the inverse scattering problem. We recover our asymptotics by transforming our problem to one which is equivalent for large time. Around the shock front the limiting "model" Riemann-Hilbert problem can be interpreted as the one corresponding to the genus 0 algebro-geometric solution of the equation. Inside the shock region, the Riemann-Hilbert problem is related to the Painlevé 4 equaton.