  In this paper, the stability of the uniform solutions is analysed for
microscopic flow models in interaction with $K\ge1$ predecessors. We calculate
general conditions for the linear stability on the ring geometry and explore
the results with particular pedestrian and car-following models based on
relaxation processes. The uniform solutions are stable if the relaxation times
are sufficiently small. The analysis is focused on the relevance of the number
of predecessors in the dynamics. Unexpected non-monotonic relations between $K$
and the stability are presented.
