  We solve the Langevin dynamics of d-dimensional ferromagnetic spherical
models with interactions that decay with distance as r^-(d+sigma). The long
time dynamics of correlations and responses are studied in the different
dynamical regimes and the validity of fluctuation-dissipation relations (or its
violation) are shown. In particular, we show that the fluctuation-dissipation
ratio X(t+t_w,t_w) is assymptotically a function only of the waiting time t_w
in the aging regime and that X -> 0 as t_w -> oo . The results are valid in any
finite dimension d and for 0 < sigma < 2, where short range behaviour is
recovered. We also solve the T=0 Cahn-Hilliard dynamics of this model
(conserved order parameter). An analysis of the multiscaling behaviour of the
autocorrelation function is presented.
