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We address the problem of non-linear transport through discrete electronic levels in a small quantum dot coupled to superconducting electrodes. In our approach the low temperature I-V characteristics can be calculated including all multiple quasi-particle and Andreev processes. The limit of very weak coupling to the leads and large charging energies is briefly analyzed comparing the calculated lineshapes of the I-V curves with recent experimental results. When the coupling to the leadsdoi:10.1103/physrevb.55.r6137 fatcat:wie6uql6jnb2dmyxnfaf7lv6ke