  Five pairs of large solar system satellites occupy first order mean-motion
resonances (MMRs). Among these, the pairs of Mimas-Tethys and Titan-Hyperion
are special. They are located much deeper in resonance than the others and
their critical arguments librate with much greater amplitudes. These
characteristics are traced to the insignificant damping, over $\Gyr$
timescales, of Mimas's orbital inclination and Hyperion's orbital eccentricity.
Absent that, these resonances would not survive. Instead their librations would
be overstable and escape from resonance would occur on the relevant damping
time. Unlike the aforementioned MMRs, those involving Enceladus-Dione,
Io-Europa, and Europa-Ganymede are limited by eccentricity damping. They must
either remain at the shallow depths they currently occupy, or, if they venture
deeper, retreat after a limited time. The latter seems almost certain for
Enceladus-Dione and quite likely for the others, We examine the MMRs involving
Mimas-Tethys and Titan-Hyperion under the assumption that they formed as a
result of convergent migration. Capture probabilities are $\sim 6\%$ for the
former and $100\%$ for the latter. The possibility of collisional excitation of
their large librations is investigated but largely discounted.
