In the last chapter attention was given to the determination of the state vector1 ξ for given observations Y and known parameters A. In this chapter the maximum likelihood estimation of the parameters \(\lambda = (\theta \prime ,\rho \prime ,\xi {\prime _0})\prime \) of an MS-VAR model is considered. The aim of this chapter is (i.) to provide the reader with an introduction to the methodological issues of ML estimation of MS-VAR models in general, (ii.) to propose with the EM algorithm an estimation technique for all discussed types of the MS-VAR models, (iii.) to inform the reader about alternative techniques which can be used for special purposes or model extensions and (iv.) to give some basic asymptotic results.