This work deals with intrinsic decay rates for the energy of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. We prove the intrinsic decay rates for the energy of a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition of relaxation kernels described by the inequality g_{i}′(t)≤-H(g_{i}(t)), (i=1,2) for all t≥0, with H convex.