We extend the three-step generalized methods of moments (GMM) approach of Kapoor et al. (2007), which corrects for spatially correlated errors in static panel data models, by introducing a spatial lag and a one-period lag of the dependent variable as additional explanatory variables. Combining the extended Kapoor et al. (2007) approach with the dynamic panel data model GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) and specifying moment conditions for various time lags, spatial lags, and sets of exogenous variables yields new spatial dynamic panel data estimators. We prove their consistency and asymptotic normality for a large number of spatial units N and a xed small number of time periods T. Monte Carlo simulations demonstrate that the root mean squared error of spatially corrected GMM estimates|which are based on a spatial lag and spatial error correction|is generally smaller than that of corresponding spatial GMM estimates in which spatial error correlation is ignored. We show that the spatial Blundell-Bond estimators outperform the spatial Arellano-Bond estimators.