Here is a possible solution using the global variable (but const for the type):
const done_function_one = Ref{Bool}(false)
function call_both()
done_function_one[] = false
@sync begin
@async begin
function_one()
done_function_one[] = true
end
@async begin
while !done_function_one[]
function_two()
end
end
end
end
, - ( ). call_both , function_two, ( function_one).