The similarity of rotation periods of the anomalous X-ray pulsars (AXPs), the soft gamma-ray repeaters (SGRs), and the dim isolated thermal neutron stars (DTNs) suggests a common mechanism with an asymptotic spin-down phase, extending through the propeller and early accretion stages. The DTNs are interpreted as sources in the propeller stage. Their luminosities arise from frictional heating in the neutron star. If the 8.4 s rotation period of the DTN RX J0720.4-3125 is close to its rotational equilibrium period, the estimated propeller torque indicates a magnetic field in the 10(12) G range. The mass inflow rate onto the propeller is on the order of the accretion rates of the AXPs. The limited range of rotation periods, taken to be close to equilibrium periods, and conventional magnetic fields in the range 5x10(11) to 5x10(12) G correspond to a range of mass inflow rates 3.2x10(14) g s(-1) < M < 4.2x10(17) Observed spin-down rates of the AXPs and SGRs also Dt in with estimates for these magnetic fields and equilibrium periods. The source of the mass inflow is a remnant accretion disk formed as part of the fallback during the supernova explosion. These classes of sources thus represent the alternative pathways for those neutron stars that do not become radio pulsars. For the highest mass inflow rates the propeller action may support enough circumstellar material so that the optical thickness to electron scattering destroys the X-ray beaming, and the rotation period is not observable. These are the radio-quiet neutron stars at the centers of supernova remnants Cas A, Puppis A, RCW 103, and 296.5+10. The statistics and ages of DTNs suggest that sources in the propeller phase are quite common, maybe accounting for the majority of neutron stars formed in supernovae. AXPs are the rare cases whose (M) over dot history has allowed them to evolve rapidly to the post-propeller accretion phase. The different classes represent alternative pathways rather than consecutive phases of evolution. Thus, for example, the AXPs are not descendants of the DTNs. This model obviates the need to postulate magnetars for AXPs and DTNs. Frequently sampled timing observations of AXPs, SGRs, and DTNs can distinguish between this explanation and the magnetar model.
