Several novel low-dimensional carbon nanomaterials, scilicet graphene mono- and bilayers, single-walled carbon nanotubes (SWNTs) and SWNTs filled with Dy@C82 endohedral metallofullerenes (metallofullerene peapods), were investigated by electrical magnetotransport measurements at low temperatures in external magnetic fields of different orientations. The highlights of this study are that for both SWNTs and metallofullerene peapods, significant negative magnetoresistance (approx. 8 to 14 %) could be observed for axially oriented magnetic fields in some of the samples, where this effect vanished...