The provision of adequate shear connection between the tension and compression-resisting components of composite flexural members is essential to the robust performance of such structural members under load. If the combined capacity of all the connections in a given composite member is to be exploited at the ultimate load of the member, there is a requirement for the connections to possess some measure of ductility, because the shear force capacities of the connections will typically be activated before the member ultimate load is attained. In this paper, finite element (FE) analyses of a composite member comprising an I-section steel beam connected to a concrete slab are used to show that the required level of connection ductility is parasitic on the compliance of the connections. In order to clearly identify the nonlinear influence of plastification of the connections on overall member behaviour, the relative properties of the connections, the slab and the beam are such that the concrete and steel exhibit little and no nonlinearity up to the peak loads here considered. The analyses reveal that, when the ultimate load of the composite member is attained, the required ductility in the connections must increase as the compliance of the connections decreases. By contrast, it is seen that, en route to attaining the ultimate load, the connection ductility required to just achieve yield of all connections increases as connection compliance increases. The implications of the FE results for the performance of steel-concrete and timber-concrete composite members at the serviceability and ultimate limit states are discussed.