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Nash-Williams proved in 1960 that a finite graph admits a $k$-arc-connectedorientation if and only if it is $2k$-edge-connected, and conjectured that thesame result should hold for all infinite graphs, too.  Progress on Nash-Williams's problem was made by C. Thomassen, who proved in2016 that all $8k$-edge-connected infinite graphs admit a $k$-arc connectedorientation, and by the first author, who recently showed thatedge-connectivity of $4k$ suffices for locally-finite, 1-ended graphs.  In the present article, we establish the optimal bound $2k$ inNash-Williams's conjecture for all locally finite graphs with countably manyends.

The Nash-Williams orientation theorem for graphs with countably many ends