A signal containing no pure sinusoidal components I'm trying to decipher what exactly this statement means.  So if I have a signal which has no pure sinusoidal components, does that mean I can't decompose my signal completely into sine-waves which may be amplitude/phase/period shifted?  And so I would conclude that there is also like a saw-tooth component or a square-function component mixed up in the signal as well?

Saying that the signal contains NO pure sinusoidal component makes me feel like its decomposition should not include ANY amplitude/phase/period shifted sine-waves.. but that seems a little extreme.

Could someone clarify this for me?  Thanks.
It contains no spikes in its frequency spectrum. (What is the Fourier transform of a sinusoid?)