  Two similar Minkowskian diffusions have been considered, on one hand by
Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]),
and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here
two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the
asymptotic behaviour of such diffusions. More generally, we establish a central
limit theorem for a class of Minkowskian diffusions, to which the two above
ones belong. As a consequence, we correct a partially wrong guess in [DH1].
