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.
