In　this　paper　we　present　and　analyze　Chebyshev　and　Legendre　pseudo-spectral　methods　for　the　second　kind　Volterra　integral　equations　with　weakly　singular　kernel　(x　-　s)(-mu),　0　＜　mu　＜　1.　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]).　Adetailed　convergence　analysis　is　carried　out,　and　several　error　estimates　in　L-infinity　and　L-omega(2)　norms　are　obtained.　Numerical　examples　are　considered　to　verify　the　theoretical　predictions.