  Low missing mass, single- and double diffraction dissociation is calculated
for the LHC energies from a dual-Regge model, dominated by a Pomeron Regge pole
exchange. The model reproduces the rich resonance structure in the low missing
mass Mx region. The diffractionly excited states lie on the nucleon trajectory,
appended by the isolated Roper resonance. Detailed predictions for the squared
momentum transfer and missing mass dependence of the differential and
integrated single- and double diffraction dissociation in the kinematical range
of present and future LHC measurements are given. The model predicts a possible
turn-down of the cross section towards, t -> 0 in a region probably accessible
in future experiments in the nearly forward direction.
  The present work is a continuation and extension (e.g. with double
diffraction) of a previous work using the dual Regge approach.
