Chemical processes are in general subject to time variant conditions because of load changes, product grade transitions, or other causes, resulting in typical nonstationary dynamic characteristic. It is of a considerable challenge for process monitoring to consider all possible operation conditions simultaneously including multifarious steady states and dynamic switchings. In this work, a novel full-condition monitoring strategy is proposed based on both cointegration analysis (CA) and slow feature analysis (SFA) with the following considerations: (1) Despite that the operation conditions may vary over time, they may follow certain equilibrium relations that extend beyond the current time, and (2) there may exist certain dynamic relations that stay invariant under normal process operation despite process may operate at different operating conditions. To monitor both equilibrium and dynamic relations, in the proposed method, nonstationary variables are separated from stationary variables first. Then by CA and SFA, the long-term equilibrium relation is distinguished from the specific relation held by the current conditions from both static and dynamic aspects. Various monitoring statistics are designed with clear physical interpretation. It can distinguish between the changes of operation conditions and real faults by checking deviations from equilibrium relation and deviations from the specific relation. Case study on a chemical industrial scale multiphase flow experimental rig shows the validity of the proposed full-condition monitoring method. (C) 2017 American Institute of Chemical Engineers