Aims. We study the kinematically distinct components in two early-type galaxies NGC448 and NGC4365 aided by integral-field observations with the Multi-Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope. The former galaxy has previously been shown to host a counter-rotating stellar disc while the latter harbours a central (apparently) decoupled core that has been suggested to not be physically distinct from the main body and instead stems from the di ff erent orbital types in the core and main body due to its triaxial nature. We aim to measure the brightness profiles, kinematics, and stellar population properties of the peculiar kinematic structures in these galaxies and shed light on their true nature and formation mechanism. Methods. We use a kinematic decomposition technique to separate the individual contributions to the spectra of the two distinct kinematic components observed at each spatial position in the field of view. Furthermore, by folding back the outcome of a photometric decomposition we reduce the intrinsic degeneracies in recovering the kinematics and the best-fitting stellar spectral templates. Finally, by extracting the Lick line-strength indices for the individual components and fitting them to single stellar population models we derive their ages, metallicities, and ff / Fe overabundances. Results. The two kinematically decoupled stellar components in NGC448 have similar ages, but di ff erent chemical compositions. The distinct kinematic feature in NGC448 has a nearly exponential surface-brightness light profile, dominates in the innermost similar to 10 0 0, is smaller in size, and is very likely an embedded counter-rotating disc as also indicated by its kinematics. It has higher metallicity than the main galaxy stellar body and lower ff / Fe overabundance. By contrast, we do not find evidence for true decoupling in the two distinct kinematic components in NGC4365. This confirms earlier work suggesting that the kinematically distinct core is likely not a separate dynamical structure, but most certainly likely a projection effect stemming from the orbital structure of this galaxy that was previously found to be intrinsically triaxial in shape. Conclusions. Our findings indicate that the kinematically decoupled component in NGC448 is truly decoupled, has external origin, and was formed through either the acquisition of gas and a subsequent star-formation episode or from the direct accretion of stars from a companion. Conversely, the presence of a kinematically distinct component in NGC4365 is not associated to a true kinematic decoupling and is instead most likely due to a projection effect stemming from the triaxial nature of this galaxy.