Asteroids in retrograde resonance with Jupiter and Saturn

We identify a set of asteroids among Centaurs and Damocloids, which orbit contrary to the common direction of motion in the Solar system and which enter into resonance with Jupiter and Saturn. Their orbits have inclinations I greater than or similar to 140 degrees and semimajor axes a < 15 au. Two objects are currently in retrograde resonance with Jupiter: 2006 BZ8 in the 2/-5 resonance and 2008 SO218 in the 1/-2 resonance. One object, 2009 QY6, is currently in the 2/-3 retrograde resonance with Saturn. These are the first examples of Solar system objects in retrograde resonance. The present resonant configurations last for several thousand years. Brief captures in retrograde resonance with Saturn are also possible during the 20 000 yr integration timespan, particularly in the 1/-1 resonance (2006 BZ8) and the 9/-7 resonance (1999 LE31).