A new general asymptotic theory of a laminar spray diffusion flame is developed using the inverse of the Zeldovitch number, theta(-1), as a small parameter. Unlike previous treatments of such flames, the current formulation is not restricted to any specific geometric flame front shape. The liquid fuel spray is assumed to evaporate in a steep front upstream of the flame front and general jump conditions across both fronts are derived. The inner structure of the flame front and conditions for its extinction are discussed. The theory is applied to two sample problems and solutions are found. Verification of the theory is achieved by its application to a spray flame theory problem from the literature and a new O(theta(-1)) correction is presented.