Delamination cracks are considered, which develop along the boundaries of different layers in a multilayered thin shell. The characteristic linear dimension of the crack in planform is assumed to be large compared with the shell thickness. A general theory suitable for materials with any inelastic properties is based on an additional boundary condition on the moving contour of the crack, which is derived by using a heuristic hypothesis. The theory of invariant Γ-integrals and the general theory of fracture are also utilized. Model experiments are indicated which enable fracture diagrams, needed for carrying the theoretical computations out to numbers, by test means to be determined. As an illustration of the general theory, a one-dimensional problem on the fracture of a two-layer beam from ideally elastic-plastic materials is studied in detail. Furthermore, the following questions are examined: the subcritical growth of delamination cracks in multilayered shells from elastic-plastic materials, the dependence of limit loads on the loading path, and delamination fatigue cracks. An exact solution is given for the problem of elliptic, parabolic, and hyperbolic cracks in a plane two-layered plate, an axisymmetric delamination crack in a two-layered cylindrical shell, and an elliptical delamination crack in a two-layered plane membrane.