Two methods of sensitivity theory, i.e., the Direct Sensitivity Approach and the Adjoint Sensitivity Method, have been successfully applied to a simplified problem of transient, one-dimensional, composite region of single-phase and homogeneous equilibrium two-phase flow within a uniformly heated channel subjected to an exponential inlet flow decay. In both methods, exact analytical solutions for all elementary sensitivity coefficients at each point in space and time are obtained. A general procedure for the construction of the sensitivity equations' boundary conditions at the moving boundary between the two phases has been developed and applied. Discontinuities in the velocity and quality sensitivity coefficients across the moving boundary have been obtained. The enthalpy sensitivity coefficients are found to be continuous. The behavior of the sensitivity coefficients has been investigated. This investigation provides insights into the relative importance of the input parameters and the nature of the propagation of uncertainties in space and time in two-phase flow systems.