Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 150; Flight Crew Total 2500; Flight Crew Type 1100
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance
Human Factors
[While] at FL350 we changed frequency to Center 100 miles north of...our intended arrival location.  We checked in at FL350 as call sign.  We then were instructed to descend to FL240; we read back clearance 'Aircraft X descend to FL240.'  At this time we descended to FL240; around FL310 we were asked if we were in the descent and responded yes and at that time was issued another descent clearance.  We landed at [our destination] uneventful.  I was notified today (four weeks later); that we checked on at FL350 and the intended descent was for a [an aircraft with a similar sounding call sign] to which we read back the clearance and descended.  ATC did not inform us it was for [another aircraft] nor did they stop us from descending or communicating to us that we had mistakenly thought it was a call to us.  We were not given a number to call upon landing.  Our crew made the mistake of responding to what we heard was [our call sign] and not confirming it was actually [for other aircraft] who we were unaware was even on frequency.  Up until today we had no idea a mishap had even taken place; it was an unfortunate place to be; considering two very similar call signs.  Both ATC and our crew is responsible and I think better communication and situational awareness can prevent other similar incidents.
A Boeing C17 flight crew inadvertently responded and complied with clearances intended for another aircraft with a similar call sign.  The flight was not advised at the time and the reporter only learned of the incident approximately a month after it occurred.