We discuss Li abundances in a well defined sample of nearby (G0-G5) so
lar-like stars. High resolution (R=100,000), high S/N (greater-than-or
-equal-to 150) data have been analysed using state-of-the-art techniqu
es and up-to-date atmospheric models. We have investigated whether the
abundance of Li in solar-type stars can be described in terms of stel
lar physical parameters like T(eff), age and metallicity. We confirm t
he presence of a group of stars with high Li content, but apparently o
ld age, finding that this group is rather conspicuous and not restrict
ed to a few exceptional cases. The analysis of our data, together with
published observations of G dwarfs in open clusters, strongly suggest
s that for stars older than approximately 1 Gyr another parameter in a
ddition to the overmentioned ones plays a relevant role in Li depletio
n. When this additional mechanism is effective, it depletes Li by a fa
ctor 10-100, but in some stars it may not act at all during a large pa
rt of their main sequence lifetimes. We make some suggestions as to th
e nature of this additional parameter but none of them can be definite
ly proven. When compared to the other stars in our sample, the Sun app
ears to be representative of the low-Li stars, which comprise about on
e half of the G dwarfs having stellar parameters and ages similar to t
he Sun. We confirm that Li is not a good tracer of age for solar-type
stars, but we show that a high Li content coupled to high chromospheri
c activity can be used to identify stars significantly younger than th
e Hyades.