  A clear evidence of inclusive diffraction observed by the CMS detector at the
Large Hadron Collider in minimum bias events at $\sqrt{s}=$0.9 TeV, 2.36 TeV is
presented. The observed diffractive signal is dominated by inclusive
single-diffractive dissociation and can be identified by the presence of a
Large Rapidity Gap that extends over the forward region of the CMS detector. A
comparison of the data with Monte Carlo predictions provided by PYTHIA6 and
PHOJET generators is given. In addition, first observation of the
single-diffractive production of di-jets at $\sqrt{s}=$7 TeV is presented.
