This　paper　is　concerned　with　the　superconvergence　of　the　discontinuous　Galerkin　solutions　for　delay　differential　equations　with　proportional　delays　vanishing　at　t　=　0.　Two　types　of　superconvergence　are　analyzed　here.　The　first　is　based　on　interpolation　postprocessing　to　improve　the　global　convergence　order　by　finding　the　superconvergence　points　of　discontinuous　Galerkin　solutions.　The　second　type　follows　from　the　integral　iteration　which　just　requires　a　local　integration　procedure　applied　to　the　discontinuous　Galerkin　solution,　thus　increasing　the　order　of　convergence.　The　theoretical　results　are　illustrated　by　a　broad　range　of　numerical　examples.