For an m-variate (“partially”) nonstationary vector autoregressive process {Yt}, we consider the autoregressive model Φ(L)Yt = εt, where Φ(L) = I − Φ1L − … − ΦpLp and det{Φ(z)} = 0 has d < m roots equal to unity and all other roots are outside the unit circle. It is also assumed that rank {Φ(1)} = r, r = m − d, so that each component of the first differences Wt = Yt − Yt − 1 is stationary. The relation of the model to error correction models and co-integration (Engle and Granger 1987) is discussed. The process {Yt} has the error correction representation Φ*(L)(1 − L)Yt = −P2(Ir − Λr)Q21Yt-1 + εt, where Q(Im − Φ(1))P = J = diag(Id, Λr) is in Jordan canonical form and Q' = [Q1, Q2]. It follows that the transformation Zt = QYt = [Zt1t, Z22t]t is such that the d × 1 process Z1t is nonstationary with Z1t − Z1t-1 stationary while Z2t is stationary. Asymptotic distribution theory for least squares parameter estimators of the model is first considered. A Gaussian partial reduced rank estimation procedure that explicitly incorporates the unit root structure in the model is then presented, and an asymptotically equivalent two-step reduced rank estimation procedure is also considered. A numerical example is presented to illustrate the methods and concepts. The finite sample properties of the estimators are also briefly examined through a small Monte Carlo sampling experiment.