This paper describes an algorithm for computing the distribution of conditional forecasts, i.e., projections of a set of variables of interest on future paths of some other variables, in dynamic systems. The algorithm is based on Kalman filtering methods and is computationally viable for large models that can be cast in a linear state space representation. We build large vector autoregressions (VARs) and a large dynamic factor model (DFM) for a quarterly data set of 26 euro area macroeconomic and financial indicators. The two approaches deliver similar forecasts and scenario assessments. In addition, conditional forecasts shed light on the stability of the dynamic relationships in the euro area during the recent episodes of financial turmoil, and indicate that only a small number of sources drive the bulk of the fluctuations in the euro area economy. (C) 2014 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.