Backward Integrations of motion of the Halley-type comets, covering over 11,000 years, are used to investigate their librations around high-order resonances with Jupiter. These occur for comets moving in direct orbits with revolution periods between 50 and 90 years. The fact that about one halí of them is librating at a time explains the concentration of revolution periods in this range. The librations are of rather uniform period and amplitude, and tend to persist over about 200 revolutions of tho comet. Their presence implies that the lifetimes of these comets since their captures Into periodlc orbits of small perihelion distance mostly exceed 300 revolutions. Possible exceptlons among the 9 comets with present periods of 50 to 90 years are the already extinct P/Westphal, and also P/Halley, for whlch a close approach to the orbit of Jupiter 150 revolutions ago was identified.