In　the　present　paper,　we　investigate　the　universal　PBW　basis　and　HN　system　for　the　derived　Hall　algebra　of　a　triangulated　category　satisfying　some　finiteness　conditions.　Furthermore,　we　study　the　related　stability　conditions　on　the　module　category　A　of　the　path　algebra　A　of　an　acyclic　quiver　and　on　the　bounded　derived　category　of　A.　Moreover,　we　investigate　the　relation　between　the　Ringel-Hall　algebra　and　the　HN　system　of　A　defined　by　Reineke.