  The $\!{}\bmod k$ chromatic index of a graph $G$ is the minimum number of
colors needed to color the edges of $G$ in a way that the subgraph spanned by
the edges of each color has all degrees congruent to $1\!\!\pmod k$. Recently,
the authors proved that the $\!{}\bmod k$ chromatic index of every graph is at
most $198k-101$, improving, for large $k$, a result of Scott [Discrete Math.
175, 1-3 (1997), 289-291]. Here we study the $\!{}\bmod k$ chromatic index of
random graphs. We prove that for every integer $k\geq2$, there is $C_k>0$ such
that if $p\geq C_kn^{-1}\log{n}$ and $n(1-p) \rightarrow\infty$ as
$n\to\infty$, then the following holds: if $k$ is odd, then the $\!{}\bmod k$
chromatic index of $G(n,p)$ is asymptotically almost surely equal to $k$, while
if $k$ is even, then the $\!{}\bmod k$ chromatic index of $G(2n,p)$
(respectively $G(2n+1,p)$) is asymptotically almost surely equal to $k$
(respectively $k+1$).
