We report the details of Sr2RuO4-Sr3Ru2O7 eutectic crystal growth by the flux-feeding floating-zone technique (FFFZ) under high pressure (lobar). Optimizing the growth conditions. we succeeded in growing eutectic crystals with a regular lamellar structure. The morphology, structure, phase purity. and composition of the crystals were analyzed by means of polarized-light optical microscopy (PLOM), X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS). This new system is expected to be usefull in the study of tunneling and proximity effects between the spin-triplet superconductor Sr2RuO4 and the metamagnetic normal metal Sr3Ru2O7. (c) 2005 Elsevier B.V. All rights reserved.