We present a systematic investigation of the possible molecular states composed of a pair of doubly charmed baryons (ΞccΞcc) or one doubly charmed baryon and one doubly charmed antibaryon (ΞccΞcc) within the framework of the one-boson-exchange-potential model. For the spin-triplet systems, we take into account the mixing between the 3 S1 and 3 D1 channels. For the baryon-baryon system ΞccΞcc with (R, I) = (3, 1/2) and (3, 0), where R and I represent the group representation and the isospin of the system, respectively, there exist loosely bound molecular states. For the baryon-antibaryon system ΞccΞcc with (R, I) = (8, 1), (8, 1/2) and (8, 0), there also exist deuteronlike molecules. The BccBcc molecular states may be produced at LHC. The proximity of their masses to the threshold of two doubly charmed baryons provides a clean clue to identify them.