Mathematical formulation and application of two sensitivity analysis methods; i.e., Direct Sensitivity Approach (DSA) and Adjoint Sensitivity Method (ASM), to the transient one-dimensional four-field equations two-phase flow diffusion model of the code COTHA is presented. A linked computer code system COTHA-COSAM is developed to evaluate sensitivity coefficients with respect to all input parameters at each point in space and time. A general procedure for calculating the appropriate sensitivity boundary conditions is developed. Initial steady-state sensitivities are evaluated automatically by running the code with prescribed constant boundary conditions. The linked COTHA-COSAM code has been tested and verified against results from simple parametric study. Typical results of a two-phase flow sample problem are presented and discussed. Some of the coefficients in the correlations of the thermodynamic properties are found to be highly "sensitive" input parameters.