  In this article we discuss several aspects of the stochastic dynamics of spin
models. The paper has two independent parts. Firstly, we explore a few
properties of the multi-point correlations and responses of generic systems
evolving in equilibrium with a thermal bath. We propose a fluctuation principle
that allows us to derive fluctuation-dissipation relations for many-time
correlations and linear responses. We also speculate on how these features will
be modified in systems evolving slowly out of equilibrium, as
finite-dimensional or dilute spin-glasses. Secondly, we present a formalism
that allows one to derive a series of approximated equations that determine the
dynamics of disordered spin models on random (hyper) graphs.
