By expanding on the principles of ideal magnetohydrodynamics (MHD), we examine the dynamics of weakly ionised astrophysical plasma flows in a multifluid regime. This numerical study is carried out using the multifluid MHD code HYDRA. An outline of the structure of this code is given in chapter 2 and the schemes which are implemented integrates the MHD equations. We are interested in multifluid effects on fluid instabilities, in particular the Kelvin-Helmholtz (KH) instability. The KH instability could, for example, play a role in the momentum transfer between the bowshock of a protostellar jet and its surrounding molecular cloud. In particular, changes to the development of the KH instability as a result of including the multlifluid effects of ambipolar diffusion and the Hall effect are isolated and individually studied in chapters 4 and 5 respectively. Finally, chapter 6 provides an in-depth examination of the respective roles these nonideal effects have in a multifluid astrophysical system in which both are expected to occur, such as a molecular cloud. Multifluid effects on protostellar jets are then examined in a broader context in chapter 7. As a jet propagates into a molecular cloud, it forms a bowshock of swept-up ambient material. As the molecular cloud material is weakly ionised, the bowshock is strongly susceptible to nonideal MHD effects below some characteristic length scale. Large-scale 3D simulations allow us to begin to understand the resulting dynamical differences in both the jet propagation and the structural evolution of the magnetic fields.