With an eye toward coded transmission of high-level modulation on satellite links, we study the information-theoretic potential of nonlinear satellite channels, for both single-user per transponder operation and simultaneous two-way, on-frequency relaying to improve spectrum efficiency as much as 100%. We develop an analytic nonlinear model with finite memory for these two scenarios, and compute achievable rate regions, i.e. information rates that are arbitrarily reliable, as a function of link SNR's and input backoff of the nonlinear amplifier. This provides guidance on required SNR and desired amplifier operating point for advanced coded modulation schemes.