The　Riemann　problem　for　the　relativistic　generalized　Chaplygin　Euler　equations　is　considered.　Its　two　characteristic　fields　are　genuinely　non-linear,　but　the　nonclassical　solutions　appear.　The　formation　of　mechanism　for　δ-shock　is　analyzed,　that　is　the　one-shock　curve　and　the　two-shock　curve　do　not　intersect　each　other　in　the　phase　plane.　The　Riemann　solutions　are　constructed,　and　the　generalized　Rankine-Hugoniot　conditions　and　the　δ-　entropy　condition　are　clarified.　Moreover,　under　the　generalized　Rankine-Hugoniot　conditions　and　entropy　condition,　we　constructively　obtain　δ　-　shock　waves.