We give two characterizations, one for the class of generalized Young measures generated by {{,mathrm{{mathcal {A}}},}}-free measures and one for the class generated by {mathcal {B}}-gradient measures {mathcal {B}}u. Here, {{,mathrm{{mathcal {A}}},}} and {mathcal {B}} are linear homogeneous operators of arbitrary order, which we assume satisfy the constant rank property. The first characterization places the class of generalized {mathcal {A}}-free Young measures in duality with the class of {{,mathrm{{mathcal {A}}},}}-quasiconvex integrands by means of a well-known Hahn–Banach separation property. The second characterization establishes a similar statement for generalized {mathcal {B}}-gradient Young measures. Concerning applications, we discuss several examples that showcase the failure of mathrm {L}^1-compensated compactness when concentration of mass is allowed. These include the failure of mathrm {L}^1-estimates for elliptic systems and the lack of rigidity for a version of the two-state problem. As a byproduct of our techniques we also show that, for any bounded open set Omega , the inclusions L1(Ω)∩kerA↪M(Ω)∩kerA,{Bu∈C∞(Ω)}↪{Bu∈M(Ω)}\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\mathrm {L}^1(\\Omega ) \\cap \\ker {\\mathcal {A}}&\\hookrightarrow {\\mathcal {M}}(\\Omega ) \\cap \\ker {{\\,\\mathrm{{\\mathcal {A}}}\\,}}\\,,\\\\ \\{{\\mathcal {B}}u\\in \\mathrm {C}^\\infty (\\Omega )\\}&\\hookrightarrow \\{{\\mathcal {B}}u\\in {\\mathcal {M}}(\\Omega )\\} \\end{aligned}$$\\end{document}are dense with respect to the area-functional convergence of measures.