The ages of two old galaxies (53W091, 53W069) at high redshifts are used to
constrain the value of the cosmological constant in a flat universe (Lambd
a CDM) and the density parameter Omega(M) in Friedmann-Robertson-Walker mod
els with no Lambda term. In the case of Lambda CDM models, the quoted galax
ies yield two lower limits for the vacuum energy density parameter, Omega(L
ambda) greater than or equal to 0.42 and Omega(Lambda) greater than or equa
l to 0.5, respectively. Although compatible with the limits from statistics
of gravitational lensing and cosmic microwave background, these lower boun
ds are more stringent than the ones recently determined using Type Ia super
novae as standard candles. For matter-dominated universes (Omega(Lambda) =
0), the existence of these galaxies imply that the universe is open with th
e matter density parameter constrained by Omega(M) less than or equal to 0.
45 and Omega(M) less than or equal to 0.37, respectively. In particular, th
ese results disagree completely with the analysis of field galaxies, which
gives a lower limit Omega(M) greater than or equal to 0.40.