  The possibility that the major part of all extrasolar hadronic cosmic rays
with energies above 10 MeV/n is of extragalactic origin is discussed. Recent
observational results on the galactocentric cosmic-ray density gradient and
very high gamma-ray emission do not support expectations from the simplest
models with a Galactic origin of cosmic rays. The hypothesis that ``flux
trapping'' of extragalactical cosmic rays occurs in the Galactic confinement
volume is advanced. Taking this phenomenon into account, I explicitely discuss
how previous objections against an extragalactic origin of hadronic cosmic rays
loose their strength. The local energy density of hadronic cosmic rays and
other observational facts can be understood in a very natural way assuming an
extragalactical origin. A promising scenario seems to be a Galactic origin of
electrons and an extragalactic origin of hadrons.
