Could the Congo Crisis (1960-65) have led to World War III?

Is there any possibility the crisis could have become a world war? If not, what's the worst it could have got, under certain circumstances? A Korea-like war? Or only a more disastrous, more bloody conflict within the borders of Congo, with limited foreign involvement?

(Bonus points if Katanga remains independent until after the war, or becomes part of the Federation of Rhodesia and Nyasaland.)
 
Is there any possibility the crisis could have become a world war?

No. Neither the U.S. nor the USSR had any essential national interest at stake.

If not, what's the worst it could have got, under certain circumstances? A Korea-like war? Or only a more disastrous, more bloody conflict within the borders of Congo, with limited foreign involvement?

The latter. There was no way for the USSR to deliver sufficient military assets to any force in central Africa to sustain a major war. Only if the superpower blocs are supporting opposing sides can there be a long term large-scale "conventional" war.
 
In theory any crisis via escalation and an unwillingness to lose face could have led to WWIII. After all an assasination in Sarajevo lead to WWI. So you could create a non-ASB timeline where things escalate and maybe even lead to WWIII.

However as the other posters have pointed out this is not a likely flashpoint since neither side in real life cared enough about it and the Soviets would have had difficulty supplying their side.
 
Whilst both the US, other Western Powers and the Soviet Union were intervening on an individual basis by supplying and supporting various factions covertly, they were all also involved in the ONUC mission to stabilise the region. A Polish medical team was present etc. Both sides wanted to maintain the appearance that they were only intervening based on legitimate principles (as part of the UN) and never really wanted to fully commit themselves, just willing to try and set up a friendly regime to do their work for them.
 
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