We report the results of Xe analyses of the eucrites Bereba, Cachari, Caldera, Camel Donga, Chervony Kut, Ibitira, Jonzac, Juvinas, Milbillillie, Moore County, Padvarninkai, Pasamonte, Pomozdino, Sioux County, and Vetluga, and the howardite Petersburg. The obtained data together with data from the literature were utilized for the calculation of PuXe ages using a modified method where the concentration of the reference element Nd (that is used in the traditional PuXe dating) is replaced by that of spallation 126Xe originating from rare earth elements. The fraction of spallation 126Xe from REE in total spallation 126Xe is calculated via the Ba/REE ratios that are very similar in different samples of a given meteorite. In comparison with the traditional PuXe dating the present method avoids problems of sampling heterogeneity and uncertainties in absolute instrument sensitivity and can be used when the concentration of Nd in a sample is not known. The PuXe ages for different samples of individual meteorites show good reproducibility. Ages of the eucrites Bouvante, Chervony Kut, Ibitira, Juvinas, Moore County, Pasamonte, PCA82502, Pomozdino, of the howardite Petersburg, and of the angrite LEW86010 are old and most likely date the time of crystallization at ∼4.56 Ga. Almost complete retention of fission Xe in these meteorites is in a stark contrast with the apparent ∼1‰ retention of radiogenic 129Xe. The eucrites Bereba, Cachari, Caldera, Camel Donga, Jonzac, Millbillillie, Neuvo Laredo, Padvarninkai, Sioux County, Stannern, and Vetluga are distinctly younger. This can be interpreted in different ways: the ages may represent crystallization and/or metamorphic ages or may simply reflect the different extent of diffusive fission Xe losses during later events. Comparison of the PuXe ages with those from the SmNd and PbPb isotope chronometers yields, in most cases, a reasonable agreement. In some meteorites, however, the PbPb chronometer appears to have been reset during secondary events while the PuXe isotope system is seen to be more resistant to such events.