On February 21, 2016, about 2015 eastern standard time, a Piper PA-28-151, N41618, was substantially damaged by an engine fire after landing at Northeast Florida Regional Airport (SGJ), St. Augustine, Florida. The flight instructor and his pilot-rated student were not injured. Night visual meteorological conditions prevailed, and no flight plan was filed for the local instructional flight, which was conducted under the provisions of Title 14 Code of Federal Regulations Part 91. According to the flight instructor, the airplane's engine stopped producing power during taxi immediately after landing. An engine restart was attempted, and the engine caught fire. The airplane was stopped, and both the instructor and the student egressed the airplane, but made no attempt to extinguish the fire, as there was no fire extinguisher on board the airplane. Instead, the instructor dialed 911 on his cellular telephone. The fire department on the airport was closed, and local police and fire responded to the call. The police arrived first, and were delayed at a perimeter gate, which was subsequently opened by airport personnel. The first police officer on scene suppressed the fire with a hand-held fire extinguisher from his cruiser until firefighters arrived and ensured the fire was fully extinguished shortly thereafter. The firefighters gained access through an entry point previously briefed and rehearsed with the airport authority. Examination of the airplane by a Federal Aviation Administration (FAA) aviation safety inspector revealed that both the engine firewall and mount required replacement due to fire damage. The inspector asked the operator why no fire extinguisher was installed in the accident airplane. He said the airplane was a late addition to the school's fleet, and that he and his staff "forgot" to install one. All other airplanes at the school were equipped with fire extinguishers. The instructor held a commercial pilot and flight instructor certificates with ratings for airplane single engine land, multiengine land and instrument airplane. His most recent third-class medical certificate was issued on January 18, 2016. The pilot reported 153 total hours of flight experience, of which 65 hours were in the accident airplane make and model. The pilot held a private pilot certificate with a rating for airplane single engine land. His most recent first-class medical certificate was issued on January 27, 2016. The instructor reported 895 total hours of flight experience, of which 20 hours were in the accident airplane make and model. The four-seat, single-engine, low-wing airplane was manufactured in 1974 and was equipped with a Lycoming O-320 series engine. A review of logbook entries by the FAA inspector revealed the airplane's most recent 100-hour inspection was completed July 27, 2015, at 7,717 total aircraft hours. Review of the Pilot's Operating Handbook, Section 3, Emergency Procedures revealed that engine fires during start were usually the result of overpriming, and that the first attempt to extinguish the fire should be to try to start the engine and draw the excess fuel back into the induction system.