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Abstract: This paper considers the two-point boundary value problem of stochastic differential equation with the following form:The sufficient and necessary conditions are given for the existence of the adapted solutions. In the simple case that f(t, X t )= f t , the solution can be obtained by introducing a control term f t , extending the solution from X t to (X t , f t ), and constructing a process sequence. All the results obtained are compared with those related to the eigenvalue problems, and the “martingale approach” solution proposed by Pardoux and Peng for backward stochastic differential equations. [Copyright &y& Elsevier]