The ageing of the European population is expected to strongly influence both the structure of family relations and the pattern of private transfers between generations. Using data from the Survey of Health, Ageing and Retirement in Europe conducted from the perspective of adults aged 50 and above in ten European countries, we provide an analysis of financial and time transfers, either given or received. Our results show that cash gifts mainly flow to the younger generations, while time transfers are directed both upwards and downwards. When comparing the countries, we find some remarkable similarity in the pattern of transfers, although there are inter-country differences. These differences sometimes follow the expected north-south European gradient, but not always. The results suggest that the social and demographic transformations currently taking place in Europe often have contradictory and paradoxical effects upon the nature of intergenerational exchanges.