The exact value of the accretion rate in novae is very important to the theory of thermonuclear runaways and nova statistics. Estimates of the typical accretion rates in nova and novalike objects are 1018g/s (1.6 10−8 M⊙/yr). Patterson (1984) estimated that if the above high accretion rate prevails the expected number of novae according to Bath and Shaviv (1976) exceeds the observed number. Prialnik, Livio, Shaviv and Kovetz (1982) have shown that no thermonuclear runaway can be obtained if the accretion rate is as high as few 10−9 M⊙/yr. Actually, the very strong thermonuclear runaways (TNRs) are obtained only for very low accretion rates namely, 10−10 to 10−11 M⊙/yr. A way out from this inconsistency was suggested by Shara, Livio, Moffat and Orio (1986) in the form of the hibernation model. In this model the high accretion rate is found only shortly before and soon after the nuclear runaway and the nova spends most of the time in a state of very low accretion rate - so low that most novae are not observed at all. The high accretion rate, according to this theory, is a precursor to the runaway. The hibernation model is very attractive in spite of a meager observational proof so far and theoretical justifications. Yet, it is one of the most promising ideas in this field. The hibernation scenario claims that the accretion rate is a function of time. It is high just prior to the runaway and it continues to be high for some time just after the runaway. It then declines to very low values. From the point of the model for the thermonuclear runaway the problem is how the star reacts to a temporary high accretion rate that comes after a long period of low accretion rate (Shaviv and Starrfield, 1987). Thus, even if the accretion rate is low during most of the time the phase of high accretion can still affect the outcome of the thermonuclear runaway.