Abstract: The modeling for more complex systems has initiated a shift away from state-space models towards models described by differential-algebraic equations(DAES).These models arise as the product of object-oriented modeling languages.The mathematics of DAES is somewhat more involved than the standard state-space theory.The introduction of stochastic signals and filtering problems into such models raises several questions of well-posed.The aim of this paper is to present a well-posed description of a linear stochastic differential-algebraic equation and explain how well-posed identification problems can be formal.System matrix is derived using the definition of good sub-space to give state conditions.As to the identification problems,we derive the Maximum Likelihood method and show how it can be efficiently implemented.