The competition between dynamical processes is an extremely relevant issue in the field of complex networks, in particular for the applications to epidemiology. Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level. In particular, interdependent contagion phenomena can be addressed only if we go beyond the scheme-one pathogen- one network. In [Sanz2014], we have proposed a framework that allows us to describe the spreading dynamics of two concurrent diseases. Specifically, we have characterized analytically the epidemic thresholds of the two diseases for different scenarios and compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease’s outbreak is conditioned to the prevalence levels of the other disease. Moreover, we have shown, for the susceptible-infected-susceptible scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the limit for scale-free networks. For the susceptible-infected-removed scenario, the phenomenology is richer and additional interdependencies show up. We have also found that the secondary thresholds for the susceptible-infected-susceptible and susceptible-infected-removed models are different, which results directly from the interaction between both diseases. Our modeling approach presents different advantages with respect to previous models, as it simultaneously allows analytical derivations of the epidemic thresholds and an approximate description of the temporal evolution of the system, in addition to providing a way to isolate the effects on spreading dynamics of each possible interaction mechanism, such as variations of infectivity, susceptibility, or infectious periods. In addition, it enables us to solve the two paradigmatic modeling scenarios (SIS and SIR), identifying relevant differences between the two cases that arise as a consequence of disease interactions.