Global G-shtukas relate to local G-shtukas as abelian varieties do to p-divisible groups. In particular, their moduli spaces are the function field analogues of Shimura varieties. Generalizations of the well-known Eichler-Shimura congruence relation have been proven for various Shimura varieties using a method introduced in the book of Faltings and Chai on degeneration of abelian varieties. In this talk, I will explain how to adapt this method to the function field setting to prove the ordinary part of the congruence relation for moduli spaces of global G-shtukas, and how the Hodge-Newton filtration fits into this picture.