In a small bowl, combine citrus peels and juices, garlic, salt, pepper and cumin. Place meat in a large zipper-topped plastic bag; add citrus mixture, seal bag and turn to evenly coat the meat. Refrigerate for 30 minutes.
Preheat grill to MEDIUM. Remove meat from marinade, discarding marinade and bag. Place tenderloin on one side of greased grill. Turn off the burners directly below the meat and cover the grill with the lid.
Grill tenderloin for 30 minutes or until cooked through, turning occasionally and brushing with barbecue sauce for the last 10 minutes of grilling time.