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We consider the consequences of an observed Cosmic Microwave Background (CMB)temperature anisotropy spectrum containing no secondary oscillations. Whilesuch a spectrum is generally considered to be a robust signature of activestructure formation, we show that such a spectrum {\em can} be produced by(very unusual) inflationary models or other passive evolution models. However,we show that for all these passive models the characteristic oscillations wouldshow up in other observable spectra. Our work shows that when CMB polarizationand matter power spectra are taken into account secondary oscillations areindeed a signature of even these very exotic passive models. We construct ameasure of the observability of secondary oscillations in a given experiment,and show that even with foregrounds both the MAP and \pk satellites should beable to distinguish between models with and without oscillations. Thus weconclude that inflationary and other passive models can {\em not} evade thesecondary oscillation test.Comment: Final version accepted for publication in PRD. Minor improvements  have been made to the discussion and new data has been included. The  conclusions are unchagne

Can inflationary models of cosmic perturbations evade the secondary oscillation test?