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We study the existence of a solution for a one-dimensional generalizedbackward stochastic differential equation with two reflecting barriers (GRBSDEfor short) under assumptions on the input data which are weaker than that onthe current literature. In particular, we construct a maximal solution for sucha GRBSDE when the terminal condition \xi is only F_T-measurable and the driverf is continuous with general growth with respect to the variable y andstochastic quadratic growth with respect to the variable z without assuming anyP-integrability conditions. The work is suggested by the interest the resultsmight have in Dynkin game problem and American game option.

Generalized BSDE With 2-Reflecting Barriers and Stochastic Quadratic Growth