Mean-field and renormalisation group theories are used to study the diagrams of anisotropic n-component d-dimensional magnetic systems with a uniaxially random magnetic field along the easy axis. For strong anisotropy only the longitudinal phase exists. The transition into this phase exhibits a tricritical point. When the anisotropy is decreased, a 'transverse' or 'spin-flopped' phase appears for low temperatures and large values of the random field. This phase is separated from the longitudinal one by a spin-flop first-order line, ending at a critical end-point. For very weak anisotropy, a bicritical point appears in the phase diagram. For a certain value of the anisotropy the critical end-point, the bicritical point and the tricritical point all coincide defining a new multicritical point.