Let (M_i,g_i)_i∈ℕ be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov–Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D^B on B. We give an explicit description of D^B and characterize the special case where D^B equals the Dirac operator on B.