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Many robotic systems, like surgical robots, robotic hands, and exoskeleton robots, use cable passing through conduits to actuate remote instruments. Cable actuation simplifies the design and allows the actuator to be located at a convenient location, away from the end effector. However, nonlinear frictions between the cable and the conduit account for major losses in tension transmission across the cable, and a model is needed to characterize their effects in order to analyze and compensate for them. Although some models have been proposed in the literature, they are lumped parameter based and restricted to the very special case of a single cable with constant conduit curvature and constant pretension across the cable only. This paper proposes a mathematically rigorous distributed parameter model for cable-conduit actuation with any curvature and initial tension profile across the cable. The model, which is described by a set of partial differential equations in the continuous time-domain, is also discretized for the effective numerical simulation of the cable motion and tension transmission across the cable. Unlike the existing lumped-parameter-based models, the resultant discretized model enables one to accurately simulate the partial-moving/partial-sticking cable motion of the cable-conduit actuation with any curvature and initial tension profile. The model is further extended to cable-conduit actuation in pull-pull configuration using a pair of cables. Various simulations results are presented to reveal the unique phenomena like backlash, cable slacking, interaction between the two cables, and other nonlinear behaviors associated with the cable conduits in pull-pull configuration. These results are verified by experiments using two dc motors coupled with a cable-conduit pair. The experimental setup has been prepared to emulate a typical cable-actuated robotic system. Experimental results are compared with the simulations and various implications are discussed.