We describe our theoretical formalism and computational scheme for making ab initio calculations of the dynamic paramagnetic spin susceptibilities of metals and alloys at finite temperatures. Its basis is time-dependent density functional theory within an electronic multiple scattering, imaginary time Green function formalism. Results receive a natural interpretation in terms of overdamped oscillator systems making them suitable for incorporation into spin fluctuation theories. For illustration we apply our method to the nearly ferromagnetic metal Pd and the nearly antiferromagnetic chromium alloy Cr95V5. We compare and contrast the spin dynamics of these two metals and in each case identify those fluctuations with relaxation times much longer than typical electronic “hopping times.”