The Pioneer 11 passage through the magnetosphere and trapped radiation of Saturn (closest approach September 1, 1979) revealed an especially intense region of high-energy particle fluxes the places unique constraints on models for sources of high-energy protons in the innermost radiation zones. Of special interest is the high-intensity flux of protons with energies >35 MeV which was measured by the University of Chicago fission cell in the inner magnetosphere between the A-Ring (2.3 Rs,Rs≡60,000 km) and the orbit of Mimas (~3 Rs). The negative phase space density gradients derived from the proton and electron observations in this region [Simpson et al., 1980; McKibben and Simpson, this issue> imply that steady-state inward diffusion from the outer magnetosphere will not be an adequate source for these high-energy protons. We have examined the possibility that this component could result from direct injection in situ by the decay of secondary neutrons produced by high-energy cosmic ray impacts on Saturn's atmosphere or rings (i.e., cosmic ray albedo neutron decay (Crand)). For the measured magnetic dipole moment of Saturn we determined from St¿rmer theory the cutoff magnetic rigidities and energies of galactic cosmic rays as a function of latitude, radial distance in the equatorial plane, and principal directions of incidence. The principal production of neutrons from Saturn's atmosphere occurs above ~60¿ latitude. Using a radial diffusion coefficient inferred from 1-MeV proton absorption measurements at the orbit of Mimas, we show that adequate by a factor of 104 to maintain the observed fluxes of protons >35 MeV in the range 2.3?L?3. We arrive at this result from two independent arguments based on injection strength and energy spectra, respectively. We also find that direct interactions of cosmic ray protons with matter in the A-, B- and C-rings fail by a factor >102 to produce a sufficient yield of neutrons. Finally we investigated the neutron production by the high-energy proton flux reported by Chenette et al. [1980> trapped on magnetic field lines passing through the lines. We proposed a relatively simple model which assumes that this trapped component originates in the secondary and tertiary production of protons by the incidence of cosmic ray protons so as to multiply the number of nuclear interactions from each primary. We found that although this assumption leads to a stronger source of netron decay protons for the inner magnetosphere, the yield still fails by at least an order of magnitude to account for the observations. However, the Crand model may be viable if the actual diffusion coefficient for <35-MeV protons is at least a factor ~10 lower than that for 1-MeV protons. The energy dependence of diffusion coefficients predicted by models of Jupiter's magnetospheric dynamics, possibly applicable to Saturn after rescaling of parameters, is discussed briefly. We discuss the problems associated with invoking neutron decay protons in the outer magnetosphere, as well as the injection of solar flare nucleons.