  Of late, there has been an upsurge of interest in studying the sequential
sharing of various forms of quantum correlations, viz., nonlocality,
preparation contextuality, coherence, and entanglement. In this work, we
explore the sequential sharing of nonlocality in a quantum network. We first
consider the simplest case of the two-input bilocality scenario that features
two independent sources and three parties, including two edge parties and a
central party. We demonstrate that in the symmetric case when the sharing is
considered for both the edge parties, the nonlocality can be shared by at most
two sequential observers per edge party. However, in the asymmetric case, when
the sharing across one edge party is considered, we show that at most, six
sequential observers can share the nonlocality in the network. We extend our
investigation to the two-input $n$-local scenario in the star-network
configuration that features an arbitrary $n$ number of edge parties and one
central party. In the asymmetric case, we demonstrate that the network
nonlocality can be shared by an unbounded number of sequential observers across
one edge party for a suitably large value of $n$. Further, we generalize our
study for an arbitrary $m$ input $n$-local scenario in the star-network
configuration. We show that even for an arbitrary $m$ input scenario, the
nonlocality can be shared by an unbounded number of sequential observers.
However, increasing the input $m$, one has to employ more number of edge
parties $n$ than that of the two-input case to demonstrate the sharing of an
unbounded number of sequential observers.
