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The increasing emphasis on the operational safety of nuclear power reactors necessitates the development of improved on-line and off-line monitoring methods during the normal plant operation. The random fluctuations in the neutron power and other system variables can be processed to extract information about sensor integrity, detection of anomalous conditions, estimation of stability margin, trend analysis, and incipient failure detection. This paper presents some of the recent developments in the areas of multivariate time series modeling and dynamic stochastic modeling with applications to both pressurized water reactors (PWRs) and boiling water reactors (BWRs). Three case studies - sensor fault detection using analytic redundancy, reactor diagnostics using multivariate spectral decomposition, and time dependent parameter estimation of BWR stability margin and steam velocity are discussed.