  We explore the modular representation theory of affine and cyclotomic
Yokonuma-Hecke algebras. We provide an equivalence between the category of
finite dimensional representations of the affine (resp. cyclotomic)
Yokonuma-Hecke algebra and that of an algebra which is a direct sum of tensor
products of affine Hecke algebras of type $A$ (resp. Ariki-Koike algebras). As
one of the applications, the irreducible representations of affine and
cyclotomic Yokonuma-Hecke algebras are classified over an algebraically closed
field of characteristic $p$. Secondly, the modular branching rules for these
algebras are obtained; moreover, the resulting modular branching graphs for
cyclotomic Yokonuma-Hecke algebras are identified with crystal graphs of
irreducible integrable representations of affine Lie algebras of type $A.$
