Calculations show that a main sequence star which is less massive than the Sun has a continuously habitable zone about it which is not only closer in than the corresponding zone about the Sun, but is also relatively narrower. Let L( t) represent the luminosity after t billion years of a main sequence star of mass M, and let rinner and router represent the boundaries of the continuously habitable zone about such a star—that is, the zone in which an Earthlike planet will undergo neither a runaway greenhouse effect in the early stages of its history nor runaway glaciation after it develops an oxidizing atmosphere. Then our computer results indicate that r outer/r inner is roughly proportional to [ L(3.5)/L(1.0)] 1/2. This ratio is smaller for stars less massive than the Sun (because they evolve more slowly), and the width of the continuously habitable zone about a main sequence star is therefore a strong function of the initial stellar mass. Our calculations show that rinner = router for M∼0.83M⊚ (i.e., K1 stars), and it therefore appears that there is no continuously habitable zone about most K stars, nor any about M stars.