Although about half of the Galactic supernova remnants 
(SNRs) are supposed to be in physical contact with 
molecular clouds (MCs), only some twenty SNRs are as 
yet known to interact with their ambient MCs with 
convincing evidences (most of which are based on the 
detection of 1720 MHz OH masers). To reveal more 
evidences of SNR-MC interaction, we are observing, and 
planning to observe, a sample of SNRs with highly 
asymmetric morphologies in CO and HCO+ molecular 
lines. This presentation will focus on the molecular 
shells 
discovered in SNRs Kes69 and Kes75. In the both SNRs, 
blue-shifted broadening in the 12CO (J=1-0) line profiles 
are found in specific LSR velocities, and molecular 
arcs/shells are found in the broadened line wings and 
are 
coincident with the SNR shells seen in centimeter radio, 
mid infrared, and X-rays. The line broadening and the 
morphological coincidence provide convincing evidence 
of the association of the SNRs with the corresponding 
MCs. 
The association leads to a determination of the 
kinematic distances to the SNRs. The multi-wavelength 
emissions 
along the shells can be accounted for by the impact of 
the SNR shocks on arc-like structures of dense, clumpy 
molecular gas. Such pre-existing structures are most 
likely to be parts of the cooled debris of the MC gas 
swept up 
by the massive progenitors' stellar winds. Thus we 
suggest that molecular shells are probably common in a 
number of SNRs.