  By a memory mean-field process we mean the solution $X(\cdot)$ of a
stochastic mean-field equation involving not just the current state $X(t)$ and
its law $\mathcal{L}(X(t))$ at time $t$, but also the state values $X(s)$ and
its law $\mathcal{L}(X(s))$ at some previous times $s<t$. Our purpose is to
study stochastic control problems of memory mean-field processes.
  - We consider the space $\mathcal{M}$ of measures on $\mathbb{R}$ with the
norm $|| \cdot||_{\mathcal{M}}$ introduced by Agram and {\O}ksendal in
\cite{AO1}, and prove the existence and uniqueness of solutions of memory
mean-field stochastic functional differential equations.
  - We prove two stochastic maximum principles, one sufficient (a verification
theorem) and one necessary, both under partial information. The corresponding
equations for the adjoint variables are a pair of \emph{(time-) advanced
backward stochastic differential equations}, one of them with values in the
space of bounded linear functionals on path segment spaces.
  - As an application of our methods, we solve a memory mean-variance problem
as well as a linear-quadratic problem of a memory process.
