A319 responds to TCAS RA while flying parallel approach to Runway 27L at ORD.

Narrative

We were cleared for the ILS Runway 27L at ORD and established on the GS and LOC outside of the OM when we received a TCAS TA for traffic to the right of us approximately 1 mile (at about the 2 O'clock position) and at the same altitude. This soon turned into a 'descend' RA. We followed the RA with a steeper descent of about 1500 FPM and held this from approximately 1500 ft AGL down to approximately 1200 ft AGL where we broke out and visually acquired the traffic; a B737; established on the ILS Runway 27R. The RA stopped about this point; but we were never given a 'clear of conflict.' The RA was reported to Tower and we corrected back to the GS by shallowing out the descent. At about 700 ft on the GS; we received another TA; which quickly became an RA of 'adjust vertical speed' based on the same traffic. Again the traffic was abeam to slightly ahead of us about 1 mile and now again roughly at our altitude in VMC. We disregarded this RA; which only lasted for approximately 10 seconds; and continued on the ILS to an uneventful landing. We never received a 'clear of conflict' after either RA.