This paper gives a formulation of 2-D adaptive parameter estimation (2-DAPE) problem in general case; when both of the 2-D space coordinates are possibly unbounded. A solution procedure is presented for this problem. In this solution procedure, the parameters of the underlying 2-D system are decomposed into two blocks, namely the horizontal and vertical blocks. The estimation of the horizontal block is made by means of a horizontal updating scheme, whereas the vertical block is to be estimated by means of a vertical updating scheme. The 2-D Lyapunov approach is employed to ensure the convergence of the presented 2-D estimation procedure. The computer simulation results are included to illustrate the effectiveness of the proposed procedure.