  We deal with a class of fully coupled forward-backward stochastic
differential equations (FBSDE for short), driven by Teugels martingales
associated with some L\'evy process. Under some assumptions on the derivatives
of the coefficients, we prove the existence and uniqueness of a global solution
on an arbitrarily large time interval. Moreover, we establish stability and
comparison theorems for the solutions of such equations. Note that the present
work extends known results by Jianfeng Zhang (Discrete Contin. Dyn. Syst. Ser.
B 6 (2006), no. 4, 927--940), proved for FBSDEs driven by a Brownian motion, to
FBSDEs driven by general L\'evy processes.
