  We review and give detailed description for ${\rm gl}_{NM}$ Gaudin models
related to holomorphic vector bundles of rank $NM$ and degree $N$ over elliptic
curve with $n$ punctures. Then we introduce their generalizations constructed
by means of $R$-matrices satisfying the associative Yang-Baxter equation. A
natural extension of the obtained models to the Schlesinger systems is given as
well.
