The crystallization age of shergottites is currently not agreed upon. Although mineral 87Rb- 87Sr, 147Sm- 143Nd, 176Lu- 176Hf, and U-Pb isochrons all give very young ages, typically in the range of 160-180 Ma, 207Pb- 206Pb data support a much older crystallization age at 4.1 Ga, which is consistent with published whole-rock 87Rb- 87Sr data on basaltic shergottites. Different isotopic systems present different complexities, but crater-counting chronology, which shows that a substantial fraction of the Martian surface was resurfaced during the late heavy bombardment, is in favor of an old Martian lithosphere with ages in accordance with Pb-Pb and Rb-Sr isotopic data. A ̃ 4.1 Ga Pb-Pb age of shergottites also agrees with the 142Nd and 182W anomalies found in these rocks and concur with the presence of an actively convecting mantle during the first 500 Myr of the planet's history. We here present new Sm-Nd, Lu-Hf, and Pb-Pb mineral isochrons for the basaltic shergottites Shergotty and Los Angeles complementing our previous results on Zagami [Bouvier A., Blichert-Toft J., Vervoort J.D. and Albarède F. (2005). The age of SNC meteorites and the antiquity of the Martian surface, Earth Planet. Sci. Lett. 240, 221-233]. The internal 147Sm- 143Nd and 176Lu- 176Hf isochrons give young ages of, respectively, 172 ± 40 (MSWD = 2.0) and 188 ± 91 (MSWD = 3.1) for Shergotty, and 181 ± 13 (MSWD = 0.14) and 159 ± 42 (MSWD = 0.01) for Los Angeles. In contrast, the Pb isotope compositions of the leached whole-rock fragments and maskelynite separates of Shergotty and Los Angeles fall on the whole-rock isochron previously established for Zagami and other shergottite samples and collectively yield a Pb-Pb age of 4050 ± 70 Ma for the crystallization of the basaltic shergottite suite. The contrast between the ̃ 170 Ma ages of internal isochrons and the 4.1 Ga age supported by Pb-Pb and 87Rb- 87Sr on whole-rocks simply reflects that the younger age dates the perturbation of a suite of rocks of Noachian age. The internal Rb-Sr, Sm-Nd, Lu-Hf, and U-Pb errorchrons are heavily biased by the presence of disseminated phosphate minerals and inclusions, for which D/H ratios ( δD~ + 4600‰) indicate strong interaction with Martian subsurface waters. In contrast, baddeleyite, occasionally present in SNCs and also having extremely young U-Pb ages, reflect resetting under the shock conditions that prevailed either during shergottite extraction from the planet or from impacts associated with a major break-up event of planetesimals in the main asteroid belt. We finally also re-examine 39Ar- 40Ar data on SNC meteorites and suggest that they as well support old crystallization ages.