  The nature of the recently detected HE and VHE gamma-ray emission of Tycho's
supernova remnant (SNR) is studied. A nonlinear kinetic theory of cosmic ray
(CR) acceleration in supernova remnants (SNRs) is employed to investigate the
properties of Tycho's SNR and their correspondence to the existing experimental
data, taking into account that the ambient interstellar medium (ISM) is
expected to be clumpy. It is demonstrated that the overall steep gamma-ray
spectrum observed can be interpreted as the superposition of two spectra
produced by the CR proton component in two different ISM phases: The first
gamma-ray component, extending up to about $10^{14}$ eV, originates in the
diluted warm ISM, whereas the second component, extending up to 100 GeV, comes
from numerous dense, small-scale clouds embedded in this warm ISM. Given the
consistency between acceleration theory and the observed properties of the
nonthermal emission of Tycho's SNR, a very efficient production of nuclear CRs
in Tycho's SNR is established. The excess of the GeV gamma-ray emission due to
the clouds' contribution above the level expected in the case of a purely
homogeneous ISM, is inevitably expected in the case of type Ia SNe.
