A non-uniform magnetic field causes an inhomogeneous distribution of magnetic grains in colloidal magnetics (so-called ferrofluids). The rate of concentration equilibrium settling is very low owing to the smallness of the particle diffusion coefficient. Therefore, if the equilibrium does not have enough time to settle, a ferrofluid behaves like a pure fluid, so that stationary convection occurs and no other. In the opposite case, that is when some non-uniform concentration profile has been formed, an oscillatory instability arises. The latter can be effectively excited under the action of a low-amplitude time-periodic magnetic field of an appropriate frequency.