  The excitation of the proton into undetected multiparticle states (double
diffraction dissociation) is an important background to single diffractive
deep-inelastic processes $ep \rightarrow e'p'\rho^{0}, ~e'p'J/\Psi, ~e'p'X$ at
HERA. We present estimates of the admixture of the double diffraction
dissociation events in all diffractive events. We find that in the $J/\Psi$
photoproduction, electroproduction of the $\rho^0$ at large $Q^2$ and
diffraction dissociation of real and virtual photons into high mass states $X$
the contamination of the double diffraction dissociation can be as large as
$\sim 30\%$, thus affecting substantially the experimental tests of the pomeron
exchange in deep inelastic scattering at HERA. We discuss a possibility of
tagging the double diffraction dissociation by neutrons observed in the forward
neutron calorimeter. We present evaluations of the spectra of neutrons and
efficiency of neutron tagging based on the experimental data for diffractive
processes in the proton-proton collisions.
