Date: 201509
Local time of day: 0601-1200
Location: ZZZ.TRACON, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Light Transport
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Ferry / Re-Positioning
Flight phase: Descent
Airspace: Class E ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: Corporate
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Confusion; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Airspace Structure; Human Factors; Procedure
Primary problem: Procedure

Narrative: Leaving FL240 ATC Center issued clearance to 8;000 feet; controller asked what our indicated airspeed was and we responded 300 KTS. This was for separation with traffic behind us who was instructed to maintain Mach .78 or less. ATC then instructed to maintain 300 KTS or greater with no clearance limit.We were handed off to approach control. We made our initial contact and within a few seconds contacting ATC advising 'We were instructed by Center to maintain 300 KTS do you still want us to do that?' The controller instructed us to simply 'Keep your speed up'. We obviously interpreted this to maintain our current speed or greater. Mindful of the usual speed restriction below 10;000 feet; I even commented to my PNF 'let's ask them about the speed. I don't want to get in trouble here'.The following controller then instructed - 'you can reduce speed now' with no mention of any speed restriction or excess speed and implied knowledge of our current speed by instructing us to reduce speed. We immediately complied.Upon landing we were asked to call TRACON for possible pilot deviation.The TRACON manager filed a pilot deviation report for travelling at a speed greater than 250 KTS in TRACON's airspace.There was never a single advisory by a TRACON controller alerting us to any speed deviation or excess speed as there normally would be in such a case. I have never encountered this situation.Additionally the controller who instructed 'Keep your speed up' implied no change in speed to us. His proper instruction to us should have been standard phraseology i.e. 'No' or 'Resume Normal Speed' if he intended for us to reduce speed and change the previous controller's clearance instructions.This situation was caused by ATC's improper nebulous instruction when asked a direct specific question regarding maintaining our last assigned speed of 300 KTS.I am well aware that there is a normal speed limit for aircraft of 250 KTS below 10;000 feet. I am also aware that ATC personnel are representatives of the Administrator employed by the FAA and issue clearances to aircraft as such. As a pilot I have no idea whether any LOA exits for TRACON to exceed this 250 knot limit. As such I comply with the instructions given by ATC; even querying such and receiving confirmation in 'keep your speed up'.


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


Synopsis: A corporate flight crew was asked to keep their speed at 300 KTS for traffic at FL240. During descent they asked the TRACON about speed and were told 'Keep it up;' then reduce. After landing they were notified a pilot speed deviation had been filed for over 250 KTS below 10;000 feet.