  We investigate the categories of finite-dimensional representations of
multicurrent and multiloop hyperalgebras in positive characteristic, i.e., the
hyperalgebras associated to the multicurrent algebras $\mathfrak
g\otimes\mathbb{C}[t_1,\ldots,t_n]$ and to the multiloop algebras $\mathfrak
g\otimes\mathbb{C}[t_1^{\pm1},\ldots,t_n^{\pm 1}]$, where $\mathfrak g$ is any
finite-dimensional complex simple Lie algebra. The main results are the
construction of the universal finite-dimensional highest-weight modules and a
classification of irreducible modules in each category. In the characteristic
zero setting we also provide a relationship between them.
