Tilted and warped discs inside tilted dark matter haloes are predicted from numerical and semi-analytical studies. In this paper, we use deep imaging to demonstrate the likely existence of tilted outer structures in real galaxies. We consider two SB0 edge-on galaxies, NGC4469 and NGC4452, which exhibit apparent tilted outer discs with respect to the inner structure. In NGC4469, this structure has a boxy shape, inclined by $Delta$PA$approx$3$^{circ}$ with respect to the inner disc, whereas NGC4452 harbours a discy outer structure with $Delta$PA$approx$6$^{circ}$. In spite of the different shapes, both structures have surface brightness profiles close to exponential and make a large contribution ($sim30$%) to the total galaxy luminosity. In the case of NGC4452, we propose that its tilted disc likely originates from a former fast tidal encounter (probably with IC3381). For NGC4469, a plausible explanation may also be galaxy harassment, which resulted in a tilted or even a tumbling dark matter halo. A less likely possibility is accretion of gas-rich satellites several Gyr ago. New deep observations may potentially reveal more such galaxies with tilted outer structures, especially in clusters. We also consider galaxies, mentioned in the literature, where a central component (a bar or a bulge) is tilted with respect to the stellar disc. According to our numerical simulations, one of the plausible explanations of such observed tilts of the bulge/bar is a projection effect due to a not exactly edge-on orientation of the galaxy coupled with a skew angle of the triaxial bulge/bar.
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