High-quality centimeter-sized single crystals of La1.2Sr1.8-yCaMn2O7 (0.0 less than or equal toy less than or equal to0.2) were successfully grown using a floating zone method associated with an image furnace. We present the growth conditions together with a characterization of the single crystals by means of optical and electron microscopy, EDX and ICP/AES analysis, DTA-TGA measurements and redox titration, X-ray powder diffraction, Laue X-ray back-reflection and neutron diffraction. We also stress the main aspects of the complex thermodynamical and kinetic behaviors of these compounds.