  Based on a recent chiral approach to nuclear matter we calculate the
in-medium interaction of nucleons at the Fermi surface $|\vec p_{1,2}|=k_f$.
The isotropic part of this quasi-particle interaction is characterized by four
density dependent (dimensionful) Fermi-liquid parameters: $f_0(k_f), f_0'(k_f),
g_0(k_f)$ and $g_0'(k_f)$. In the approximation to $1\pi$-exchange and iterated
$1\pi$-exchange (which as such leads already to a good nuclear matter equation
of state) we find a spin-isospin interaction strength of $g_0'(2m_\pi) = 1.14
$fm$^2$, compatible with existing empirical values. In the next step we include
systematically the contributions from $2\pi$-exchange with virtual
$\Delta(1232) $-isobar excitation which have been found important for good
single-particle properties and spin-stability of nuclear matter. Without any
additional short distance terms the spin-dependent Fermi-liquid parameters
$g_0(k_{f0})$ and $g'_0(k_{f0})$ come out far too large. Estimates of these
short-distance parameters from realistic NN-potentials go in the right
direction, but sizeable enhancement factors are still needed to reproduce the
empirical values of $g_0(k_{f0})$ and $g_0'(k_{f0})$. This points towards the
importance of higher order iterations subsumed in the induced interaction. We
consider also the tensor part of the quasi-nucleon interaction at the Fermi
surface. In comparison to the leading $1\pi$-exchange tensor interaction we
find from the $2\pi$-exchange corrections almost a doubling of the isoscalar
tensor strength $h_0(k_f)$, whereas the isovector tensor strength $h_0'(k_f)$
is much less affected. These features are not changed by the inclusion of the
chiral $\pi N\Delta$-dynamics.
