The Temporal Constraint Satisfaction Problem with Uncer-tainty (TCSPU) and its disjunctive generalization, the Dis-junctive Temporal Problem with Uncertainty (DTPU), are quantitative models for temporal reasoning that account si-multaneously for disjunctive constraints and for events not under the control of the executing agent. Such a problem is Weakly Controllable if in each possible scenario the agent can find a decision for that scenario that satisfies all the con-straints; further, a problem is Dynamically Controllable if the agent can build a consistent decision online, as the scenario is incrementally revealed. We first consider Weak Control-lability. We present two sound and complete algorithms for checking Weak Controllability of DTPUs. The first algorithm needs to examine only a limited number of scenarios, but op-erates only on a restricted class of problems. The second al-gorithm is fully general, but is more expensive in terms of space. We then consider Dynamic Controllability. We present a complete algorithm for testing this property for TCSPUs. Complexity results are presented for all three algorithms.