The global phase diagram of the S=1 Ising model in a transverse field is studied using a mean-field approximation. The critical behavior has also been considered by real-space renormalization-group techniques. This model is used to analyze the phase diagram of weakly coupled (J J <<1) classical Blume-Emery-Griffith chains. It is found that such systems display a first-order transition only in a very limited range of their parameters. © 1981 The American Physical Society.