  We study the behaviour of two Brownian particles coupled by an elastic
harmonic force in a quenched disordered medium. We found that to first order in
disorder strength, the relative motion weakens (with respect to the reference
state of a Brownian particle with the double mass) the effect of the quenched
forces on the centre of mass motion of the Brownian particles, so that the
motion will become less subdiffusive (superdiffusive) for potential
(solenoidal) disorder. The mean-square relative distance between the particles
behaves in a different way depending of whether the particles are free to move
or one particle is anchored in the space. While the effect of nonpotential
disorder consists in increasing the mean-square distance in both cases, the
potential disorder decreases the mean-square distance, when the particles are
free to move, and increases it when one particle is anchored in the space.
