A set of portable/transportable X-ray analytical instruments based on radiography, microtomography, fluorescence and diffraction have been built and are being operated at the Multidisciplinary Laboratory (MLAB) of the ‘Abdus Salam’ International Centre for Theoretical Physics (ICTP) in collaboration with Elettra-Sincrotrone Trieste. This is part of a project funded by the Region Friuli Venezia Giulia (Italy) and the ICTP, which aims to develop innovative X-ray analytical tools for noninvasive studies of cultural heritage objects and palaeontological remains. The X-ray instruments at MLAB are also used for hands-on training activities involving students and scientists from developing countries. The MLAB analytical tools complement the microtomography instruments available at Elettra-Sincrotrone Trieste. Examples of our first studies in archaeological and palaeontological applications are presented here.