The Union??? Including Haiti, Brazil, San Marino, etc who made little if any contribution to WWI and then to lump Australia, Canada, etc into the British Empire is just wrong. And if we are to include all nations involved however small in a war, you need to include Australia, New Zealand, Thailand, South Korea, Taiwan, North Korea, China, USSR, Cuba, Thailand, Philippines, Laos, and Cambodia.
Should probably specify which civil war, as there've been civil wars in the US, Spain, Sudan, Ireland, and loads of other countries, so I had no idea which one this was on about :P
http://en.wikipedia.org/wiki/Vietnam_War#Other_countries.27_involvement