In　this　paper　we　present　and　analyze　Chebyshev　and　Legendre　pseudo-spectral　methods　for　the　second　kind　Volterra　integral　equations　with　weakly　singular　kernel　(Formula　presented.).　The　proposed　methods　are　based　on　the　Gauss-type　quadrature　formula　for　approximating　the　integral　operators　involved　in　the　equations.　The　present　work　is　an　extension　of　the　earlier　proposed　spectral　Jacobi–Galerkin　method　for　the　second　kind　Volterra　integral　equations　with　regular　kernels　(Xie　et　al.　in　J　Sci　Comput　53(2):414–434,　[21]).　A　detailed　convergence　analysis　is　carried　out,　and　several　error　estimates　in　(Formula　presented.)　and　(Formula　presented.)　norms　are　obtained.　Numerical　examples　are　considered　to　verify　the　theoretical　predictions.　©　2015,　Springer　Science+Business　Media　New　York.