B737 Undifferentiated or Other Model
Flight Crew Last 90 Days 32; Flight Crew Total 7698; Flight Crew Type 4584
Conflict Airborne Conflict
Flight Crew Took Evasive Action; Flight Crew FLC complied w / Automation / Advisory
Human Factors; Procedure
We were level at FL350 and in communication with Merida Center on 125.80. At 16 NM north of DUSLO intersection on UB753; we noticed traffic on the TCAS.  Almost immediately; the traffic icon changed to amber and was climbing into our altitude. ATC had not issued any notice and we poised ourselves for corrective action while trying to identify the target visually as it was clear and VMC. The intruder aircraft was traveling from east to west. Upon receiving the TCAS RA; we responded per Company procedure and climbed according to the TCAS direction.  We reached 35;520 feet at which time we were alerted that we were clear of the conflicting aircraft. We then notified ATC and returned to our previously cleared altitude of FL350 and re-established the proper level of automation for the phase of flight.
While in level cruise flight (VMC) at 35;000 on UB753 North of DUSLO intersection; converging traffic was noticed on TCAS just 400 feet below at our 11 o'clock position. I was the pilot monitoring and both the first officer and I noticed the TCAS traffic at the same time. I verbally stated 'get ready; this one is real' to the first officer. Two seconds later; as the aircraft continued to climb; we received the Climb resolution advisory. The first officer disconnected the autopilot and smoothly climbed to 35;520 feet as the aircraft passed below us. The execution was flawless and smooth enough that it went unnoticed by cabin crew and passengers. I announced our intentions to MMID Center (125.8) and received an unconcerned 'Roger.' The MID Center controller was working this commercial traffic but the conversation was in Spanish. No explanation was given and our flight progressed with no further incident.
B737 flight crew experiences a TCAS RA at FL350; 16 NM north of DUSLO Intersection on UB753. A climb is initiated in compliance with the RA and the event reported to Merida Center.