  Let $H=(V,E)$ be a hypergraph, where $V$ is a set of vertices and $E$ is a
set of non-empty subsets of $V$ called edges. If all edges of $H$ have the same
cardinality $r$, then $H$ is a $r$-uniform hypergraph; if $E$ consists of all
$r$-subsets of $V$, then $H$ is a complete $r$-uniform hypergraph, denoted by
$K_n^r$, where $n=|V|$. A $r$-uniform hypergraph $H=(V,E)$ is
$(k,l)$-edge-maximal if every subhypergraph $H'$ of $H$ with $|V(H')|\geq l$
has edge-connectivity at most $k$, but for any edge $e\in E(K_n^r)\setminus
E(H)$, $H+e$ contains at least one subhypergraph $H''$ with $|V(H'')|\geq l$
and edge-connectivity at least $k+1$. In this paper, we obtain the lower bounds
and the upper bounds of the sizes of $(k,l)$-edge-maximal hypergraphs.
Furthermore, we show that these bounds are best possible. Thus prior results in
[Y.Z. Tian, L.Q. Xu, H.-J. Lai, J.X. Meng, On the sizes of $k$-edge-maximal
$r$-uniform hypergraphs, arXiv:1802.08843v3] are extended.
