The strong decays of the pseudoscalar and scalar double-charmed tetraquarks T + cc;ud and T + cc;ud are investigated in the framework of the QCD sum rule method. The mass and coupling of these exotic four-quark mesons are calculated in the framework of the QCD two-point sum rule approach by taking into account vacuum condensates of the quark, gluon, and mixed local operators up to dimension 10. Our results for masses mT = (4130 ±170) MeV and m T = (3845 ±175) MeV demonstrate that these tetraquarks are strong-interaction unstable resonances and decay to conventional mesons through the channels T + cc;ud → D + D * (2007) 0 , D 0 D * (2010) + and T + cc;ud → D + D 0 . Key quantities necessary to compute the partial width of these decay modes, i.e., the strong couplings of two D mesons and a corresponding tetraquark gi, i = 1, 2, and G are extracted from the QCD three-point sum rules. The full width ΓT = (129.9 ± 23.5) MeV demonstrates that the tetraquark T + cc;ud is a broad resonance, whereas the scalar exotic meson with Γ T = (12.4 ± 3.1) MeV can be classified as a relatively narrow state.