Based upon Lekhnitskii``s formulation and Stroh formalism for plane elasticity theory of an anisotropic body, the asympototic solution is examined for a delamination crack in a laminated composite strip undergoing generalized plane deformation under extension, bending and/or torsion. The near-field conditions for the opened and the closed delamination crack are imposed, together with the eigenfunction expansion for the displacement potential, to lead to the structure of solutions which consist of homogeneous solution and particular solution. It appears that no logarithmic solutions exist, regardless of the ply orientations, for each of an opened and a closed crack, and thus power type homogeneous solution and the polynomial type particular solution turn out to be valid.