In this paper a search for associated charm production both in neutral and charged current nu-nucleus interactions is presented. The improvement of automatic scanning systems in the CHORUS experiment allows an efficient search to be performed in emulsion for short-lived particles. Hence a search for rare processes, like the associated charm production, becomes possible through the observation of the double charm-decay topology with a very low background. About 130000 nu. interactions located in the emulsion target have been analysed. Three events with two charm decays have been observed in the neutral-current sample with an estimated background of 0.18 +/- 0.05. The relative rate of the associated charm cross-section in deep inelastic. interactions, sigma(c (c) over barv)/sigma(DIS)(NC) = (3.62(-2.42)(+2.95)(stat)+/-0.54(sysyt))x10(-3) has been measured. One event with two charm decays has been observed in charged-current nu(mu) interactions with an estimated background of 0.18 +/- 0.06 and the upper limit on associated charm in charged- current interactions at 90% C. L. has been found to be sigma(c (c) over bar mu(-))/sigma(CC) < 9.69 x 10(-4).