  We present results of high-resolution thermal-expansion and specific-heat
measurements on single crystalline alpha'-NaV2O5. We find clear evidence for
two almost degenerate phase transitions associated with the formation of the
dimerized state around 33K: A sharp first-order transition at T1=(33+-0.1)K
slightly below the onset of a second-order transition at T2onset around
(34+-0.1)K. The latter is accompanied by pronounced spontaneous strains. Our
results are consistent with a structural transformation at T1 induced by the
incipient spin-Peierls (SP) order parameter above T2=TSP.
