Recently, it was suggested that the two main problems of the Standard Model could be related to the phenomenon of neutrino oscillations, which discovery led to the Nobel prize for physics in 2015 given to T. Kajita and A. B. McDonald. This discovery seems to suggest the existence of particular kind of neutrinos known as Majorana neutrinos, which are not present in the Standard Model. Adding three Majorana neutrinos to the Standard Model particles, one for each of the Standard Model neutrinos, can explain the asymmetry between matter and anti-matter in the Universe and the existence of Dark Matter. In addition, these new particles would explain the reason why Standard Model neutrinos are much lighter than other matter particles. Majorana neutrinos would interact very weakly, and they are therefore very difficult to detect. In addition, many other models that explain Dark Matter by postulating the existence of very weakly interacting particles have been proposed in recent years. In this project I propose to search for these particles at the upgrade of the LHCb experiment, at the Large Hadron Collider of CERN and at the newly proposed SHiP experiment, of which I am one of the main proponents.