The FAI dealt with aeromodelling for the first time at the 1935 Dubrovnik Conference when the Aero Club of France proposed a first set of rules to cover national and international records. The first ever world record, called international records at that time, to be recognised was a duration of 7 minutes and 36 seconds set by Mr. Gabriel Robert from France on 13 September 1936. This record was set using a free flight model with extensible motor in what was at that time 'Category A' (hand launched models).
Since then, hundreds, if not thousands of world records have been set, pushing the capabilities of model aircraft beyond limits nobody would have dreamt of some decades ago. Model aircraft have flown for more than 30 hours, reached altitudes in excess of 8000 metres and covered distances of more than 1300 km.
Text above from the search page for aeromodelling Records:- http://www.fai.org/aeromodelling/records/
More than 30 Hours
Nick Shaw from ISA flew an Eliminator 134 at Ivinghoe Beacon on the 7-8 September 2001 for 36 hours 3 minutes and 19 seconds - more than doubling the existing British record and beating the world duration record for ANY model flight (not just slope duration). This flight was ratified at the BMFA Technical Council Meeting on 27th October 2001 as British record and recognised by the FAI as a world record on 21st November 2001. Full details and pictures at Mike Shellim's RC-Soaring.