We discuss frequency standards based on laser-cooled Hg-199(+) ions co
nfined in cryogenic rf (Paul) traps. In one experiment, the frequency
of a microwave source is servoed to the ions' ground-state hyperfine t
ransition at 40.5 GHz. For seven ions and a Ramsey free precession tim
e of 100 s, the fractional frequency stability is 3.3 (2) x 10(-13) ta
u(-1/2) for measurement times tau < 2 h. The ground-state hyperfine in
terval is measured to be 40507347996.84159(20)(41) Hz, where the first
number in parentheses is the uncertainty due to statistics and system
atic effects, and the second is the uncertainty in the frequency of th
e time scale to which the standard is compared. In a second experiment
under development, a strong-binding cryogenic trap will confine a sin
gle ion used for an optical frequency standard based on a narrow elect
ric quadrupole transition at 282 nm. The bandwidth of the laser used t
o drive this transition is less than 10 Hz at 563 nm.