Single crystals of CeSix (x = 1.79 - 1.85) with an orthorhombic structure have been grown by floating zone methods both with RE induction and optical heating at feed rod compositions CeSiy (y = 1.76-1.89). High-perfection single crystals were achieved for a narrow composition interval y = 1.81 - 1.82. A slight axial segregation of Si in the crystal and 2nd phase inclusions of Si (y > 1.82) and of CeSi (y < 1.80), have been detected outside this interval. From the results to the crystal growth modifications of the current Ce-Si phase diagram are inferred. The control of oxygen trace element content, which may cause constitutional supercooling, is another crucial problem of the growth process. Measurements of physical properties on CeSi1.81 single crystals show a second-order phase transition to strong easy-plane ferromagnetic order at T-C approximate to 9.5 K, whereas the c-axis is the hard axis. (C) 2004 Elsevier B.V. All rights reserved.