https://travel.state.gov/content/travel/en/legal/travel-legal-considerations/Advice-about-Possible-Loss-of-US-Nationality-Dual-Nationality/Loss-US-Nationality-and-Foreign-Military-Service.html
They'll show up as "support", "trainers", or "advisors" when they're actively directing foreign troops, making them in effect Non-Commissioned Officers (NCOs) or Officers, both of which ARE expatriating acts.