The objective of this paper is to provide a simple model that can explain the long-run fluctuations of the annual flow of inheritance as identified by Piketty (2011) for France and Atkinson (2018) for the UK. We consider a two-sector Barro-type (1974) OLG model with non-separable preferences and bequests. The local stability properties of the optimal path apprear to depend on preferences through the sign of the cross derivative of the utility function, and on technologies through the sign of the capital intensity difference across the two sectors. We show in a first part that, under the assumption of a non-strictly concave utility function, preference and technology mechanisms can be separated and lead, each of them, to the existence of period-two cycles if the life-cycle utility function has a positive cross derivative across periods, and /or the consumption good is more capital intensive than the investment good. In a second part, considering a strictly concave utility function, the preference and technology mechanisms are now combined and can lead to the existence of quasi-periodic cycles through a Hopf bifurcation if the life-cycle utility function has a positive cross derivative across periods AND the consumption good is more capital intensive than the investment good. We also show that all these results are compatible with positive bequests.