We present high-precision Mg isotope data for most classes of basaltic meteorites including eucrites, mesosiderite silicate clasts, angrites and the ungrouped Northwest Africa (NWA) 2976 measured by pseudo-high-resolution multiple-collector inductively coupled plasma mass spectrometry and utilising improved techniques for chemical purification of Mg. With the exception of the angrites Angra dos Reis, Lewis Cliff (LEW) 86010, NWA 1296 and NWA 2999 and the diogenite Bilanga, which have either been shown to have young ages by other dating techniques or have low Al/Mg ratios, all bulk samples of basaltic meteorites have (26)Mg excesses (delta(26)Mg* = +0.0135 to +0.0392 parts per thousand). The (26)Mg excesses cannot be explained by analytical artefacts, cosmogenic effects or heterogeneity of initial (26)Al/(27)Al, Al/Mg ratios or Mg isotopes in asteroidal parent bodies as compared to Earth or chondrites. The (26)Mg excesses record asteroidal melting and formation of basaltic magmas with super-chondritic Al/Mg and confirm that radioactive decay of short-lived (26)Al was the primary heat source that melted plane-testimals. Model (26)Al-(26)Mg ages for magmatism on the eucrite/mesosiderite, angrite and NWA 29 (7) over bar6 parent bodies are 2.6-3.2, 3.9-4.1 and 3.5 Myr, respectively, after formation of calcium aluminium-rich inclusions (CAIs). However, the validity of these model ages depends on whether the elevated Al/Mg ratios of basaltic meteorites result from magma ocean evolution on asteroids through fractional crystallisation or directly during partial melting. Mineral isochrons for the angrites Sahara (Sah) 99555 and D'Orbigny, and NWA 2976, yield ages of 5.06(-0.05)(+0.06) Myr and 4.86(-0.09)(+0.10) Myr, respectively, after CAI formation. Both isochrons have elevated initial delta(26)Mg* values. Given the brecciated and equilibrated texture of NWA 2976 it is probable that its isochron age and elevated initial delta(26)Mg*(+0.0175 +/- 0.0034 parts per thousand) reflects thermal resetting during an impact event and slow cooling on its parent body. However, in the case of the angrites the marginally elevated initial d(26)Mg* (+0.0068 +/- 0.0058%) may reflect either delta(26)Mg* ingrowth in a magma ocean prior to eruption and crystallisation or in an older igneous protolith with super-chondritic Al/Mg prior to impact melting and crystallisation of these angrites, or partial internal re-equilibration of Mg isotopes after crystallisation. (26)Al-(26)Mg model ages and an olivine + pyroxene + whole rock isochron for the angrites Sah 99555 and D'Orbigny are in good agreement with age constraints from (53)Mn-(53)Cr and (182)Hf-(182)W short-lived chronometers, suggesting that the (26)Al-(26)Mg feldspar-controlled isochron ages for these angrites may be compromised by the partial resetting of feldspar Mg isotope systematics. Even when age constraints from the (26)Al-(26)Mg m angrite model ages or the mafic mineral + whole rock isochron are considered, the relative time difference between Sah 99555/D'Orbigny crystallisation and CAI formation cannot be reconciled with Pb-Pb ages for Sah 99555/D'Orbigny and CAIs, which are ca. 1.0 Myr too old (angrites) or too young (CAIs) for reasons that are not clear. This discrepancy might indicate that (26)Al was markedly lower (ca.

40%) in the planetesimal-and planet-forming regions of the proto-planetary disc as compared to CAIs, or that CAI Pb-Pb ages may not accurately date CAI formation, which might be better dated by the (182)Hf-(182)W and (26)Al-(26)Mg m chronometers as 4568.3 +/- 0.7 (Burkhardt et al., 2008) and 4568.5 +/- 0.3 Ma (herein), respectively, when mapped onto an absolute timescale using Pb-Pb ages for angrites.