EMB-505 / Phenom 300
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors; Procedure
ATC rerouted us and changed fixes. They cleared us to DERLO and we typed in DELRO in the FMS; no significant changes appeared. We thought we were heading in the right direction.  ATC queried us about where we heading; we told them DELRO; they then re spelled the fixed and we proceeded to DERLO. Caused by a typo in FMS and two fixes sounding the same. Typed in the correct fix and proceeded to DERLO. Should always have the phonetic spelled from ATC and type in the correct letters.
EMB505 Captain reported being cleared to DERLO but DELRO was entered into the FMC. ATC detected the error and reissued the clearance.