This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. The paper is organized as follows: The first section is an introduction. In Section 2, the model problem in a mixed formulation is presented. Its well-posedness for Robin boundary conditions is proved in Section 3. In Section 4, the equivalent multidomain is introduced using nonoverlapping domain decomposition and two solution methods are described. A convergence proof for the optimized Schwarz waveform relaxation algorithm for the mixed formulation is given. In Section 5, the semidiscrete problems in time using different time grids in the subdomains are considered. Numerical results for two-dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods in Section 6. Finally, some concluding remarks are given in Section 7.