Usually, when two armies of different nations are in close proximity to each other, it is for good reason. For example,
They are at war with each other;
There are tensions between their nations and they are massing at their borders in case of war with each other;
They are allied with one another (perhaps they are at war with a common enemy; perhaps they are exercising together, etc.); or
Even if they are not allied, they are at war with a common enemy.
I'm curious to hear about historical instances where, by contrast, two armies just happened to be near each other by coincidence, especially if they were each at war with different enemies.