This paper presents a unified approach for the quantification of feasibility and flexibility of systems that operate dynamically under the effect of time-varying uncertainty. Based on the steady state flexibility analysis framework, the formulation for both the dynamic feasibility and dynamic flexibility analysis problems is developed. It is shown that when the assumption of given uncertainty profile holds, both problems reduce to dynamic optimization problems that can be solved using currently available techniques. For the case when this assumption is not valid, a discretization scheme for the differential equations is combined with an active constraint strategy to transform both problems into mixed integer nonlinear programming problems. A number of examples are used to illustrate the applicability of the proposed framework.