Date: 201411
Local time of day: 1201-1800
Location: ZZZ.ARTCC, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Learjet 25
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Ferry / Re-Positioning
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Aircraft component: Pressurization System
Component problem: Malfunctioning
Reporter organization: Personal
Reporter function: First Officer; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Multiengine
Human factors: Situational Awareness
Second reporter function: Captain; Pilot Flying
Anomaly: Aircraft Equipment Problem Critical; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft Other Automation; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Overcame Equipment Problem; Flight Crew Returned To Clearance
Contributing factors: Aircraft; Human Factors
Primary problem: Aircraft

Narrative: While cruising at flight level 410 about 80 miles from ZZZZZ intersection we experienced a rapid decompression immediately donned the oxygen mask and commenced a rapid descent notifying ATC simultaneously that we were descending to FL270. ATC queries if we were declaring an emergency at which we said no; knowing that at lower altitude we could reset the bleed valves; and if we couldn't reset the valves it would have become an emergency. Communication with ATC at this time was very difficult due to the warning aural sounds in the cockpit. During the rapid descent the autopilot was reengaged and the altitude selector was selected to flight level 270; on reaching flight level 270 the autopilot failed to capture the selected altitude because of the excessive nose down attitude. We eventually leveled off at flight level 265 at which time the autopilot began porpoising. ATC queried our altitude assigning us an altitude of FL250 and an immediate 40 degree left turn and ask us why we couldn't have maintained FL270. At which time we told them we were having issues with our autopilot. We reset the bleed valve thus correcting the pressurization issues and requested to climb to flight level 410. Our supplemental oxygen was used for the remainder of the flight. Upon reaching flight level 410 the autopilot began porpoising between 300 to 400 feet. It did that for the next 30 minutes at which time it stopped and the rest of the flight went uneventful. We were told to call the center telephone number as we could have been involved in a possible pilot deviation. We promptly made that call upon arriving our destination.


Second narrative: [Report narrative contained no additional information].


Synopsis: Lear 25 flight crew experiences a rapid decompression at FL410 and initiates an immediate emergency descent but does not declare an emergency; even when queried by ATC. The bleed valves are successfully reset at FL270 and the crew returns to FL410 using supplemental oxygen for the remainder of the flight.