  The two component model describes neutron star dynamics incorporating the
response of the superfluid interior. Conventional solutions and applications
involve constant external torques, as appropriate for radio pulsars on
dynamical timescales. We present the general solution of two component dynamics
under arbitrary time dependent external torques, with internal torques that are
linear in the rotation rates, or with the extremely non-linear internal torques
due to vortex creep. The two-component model incorporating the response of
linear or nonlinear internal torques can now be applied not only to radio
pulsars but also to magnetars and to neutron stars in binary systems, with
strong observed variability and noise in the spin-down or spin-up rates. Our
results allow the extraction of the time dependent external torques from the
observed spin-down (or spin-up) time series, $\dot{\Omega}(t)$. Applications
are discussed.
