A small proportion of elliptical and lenticular galaxies show evidence of well-defined dust-lanes when examined on deep survey plates. New near-infrared (JHK) observations of 46 dust-lane galaxies are presented and compared with those for a sample of 24 morphologigally normal systems. Infrared excesses are found preferentially in galaxies which exhibit at least weak signs of a stellar disc ; the physics of the emission mechanism is discussed in the light of additional 3.5 y observations and published optical spectra. The most extreme properties are those of the heavily obscured edge-on galaxy NGC7172. In this case, the infrared emission is variable on a timescale ^0.5 yrs. New optical spectra are also discussed and support the identification of the hard X-ray source H2158-321 with this galaxy. A restricted sample of 'elliptical-like' galaxies with dust-lanes, but containing no significant luminous disc, has been defined. It is demonstrated that these galaxies cannot be distinguished from a comparable sample of morphologically normal ellipticals on the basis of UBV colours or luminosity. Four examples have been selected for a detailed study of their structure and dynamics. Rotation curves and velocity dispersion profiles have been derived from long-slit spectra using Fourier analysis techniques ; surface photometry was obtained from large-scale photographic plates. The data reduction and analysis techniques are discussed in some detail. In three cases the angular momentum axis of the dust-lane is different from that of the stellar component, favouring an external origin for the dust and gas. Two of the galaxies rotate as rapidly as oblate models with isotropic velocity dispersions ; this property is characteristic. of the luminous bulges in disc systems. The orientation of the dust-lane favours a prolate geometry for one of these bulges. It is demonstrated that the kinematics are inconsistent with two recently published models of prolate.galaxies.