Pluripotency and proliferative capacity of human embryonic stem cells (hESCs) make them a promising source for basic and applied research as well as in therapeutic medicine. The introduction of human induced pluripotent cells (hiPSCs) holds great promise for patient-tailored regenerative medicine therapies. However, for hESCs and hiPSCs to be applied for therapeutic purposes, long-term genomic stability in culture must be maintained. Until recently, G-banding analysis was considered as the default approach for detecting chromosomal abnormalities in stem cells. Our goal in this study was to apply fluorescence in-situ hybridization (FISH) and comparative genomic hybridization (CGH) for the screening of pluripotent stem cells, which will enable us identifying chromosomal abnormalities in stem cells genome with a better resolution. We studied three hESC lines and two hiPSC lines over long-term culture. Aneuploidy rates were evaluated at different passages, using FISH probes (12,13,16,17,18,21,X,Y). Genomic integrity was shown to be maintained at early passages of hESCs and hiPSCs but, at late passages, we observed low rates mosaiciam in hESCs, which implies a direct correlation between number of passages and increased aneuploidy rate. In addition, CGH analysis revealed a recurrent genomic instability, involving the gain of chromosome 1q. This finding was detected in two unrelated cell lines of different origin and implies that gains of chromosome 1q may endow a clonal advantage in culture. These findings, which could only partially be detected by conventional cytogenetic methods, emphasize the importance of using molecular cytogenetic methods for tracking genomic instability in stem cells.