  We consider magnetic breakdown in twisted bilayer graphene where electrons
may hop between semiclassical $k$-space trajectories in different layers. These
trajectories within a doubled Brillouin zone constitute a network in which an
$S$-matrix at each saddle point is used to model tunneling between different
layers. Matching of the semiclassical wavefunctions throughout the network
determines the energy spectrum. Semiclassical orbits with energies well below
that of the saddle points are Landau levels of the Dirac points in each layer.
These continuously evolve into {\it both} electron-like and hole-like levels
above the saddle point energy. Possible experimental signatures are discussed.
