From near-infrared, narrow-band photometry of 256 oxygen-rich Mira variables we obtain evidence about the loops that these stars follow in colour-colour diagrams. We also find a phase lag between indices related to molecular band-strength of titanium oxide and vanadium oxide. We compute colours for normal M-giants and Miras using hydrostatic and hydrodynamic model atmospheres and very extensive up-to-date line lists. Normal M-giants colours are well reproduced, reaching a high quantitative agreement with observations for spectral types earlier than M7. The out-of-phase variations of the various spectral features of Miras are also acceptably reproduced, despite limitations in the modelling. This enables us to confirm that the phase lag phenomenon results from the propagation of perturbations in the extended atmosphere. It opens new perspectives in the spectral modelling of Miras.
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