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U.S. airstrike kills top Iran general, Qassem Soleimani, at Baghdad airport

The Defense Department said in announcing the strike Thursday night that Soleimani had orchestrated attacks on coalition bases in Iraq ...

There is info on the sidebar of this Wikipedia page, but many of the cited sources are years old.

Which "coalition" countries currently have troops in Iraq and how many ?

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Germany has about 90 troops in northern Iraq (German news report from today).

The UK has less than 400 troops in Iraq (BBC news report, 400 troops in the Middle East, an unspecified number of troops and 400 other personnel in Iraq -> less than 400 troops in Iraq).

There may be others, those were in the news I've read recently.

  • News today is that 120 (not 90) Germans have interrupted their training mission due to the events. The report was not clear if they were going to leave or just staying in their camps. – o.m. Jan 4 at 6:04
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France pulled its artillery units (Task Force Wagram) in May 2019. There are still about 100 French soldiers as part of the TF Monsabert training and supporting the Iraqi 6th division and a few more as part of the TF Narvik training the Iraqi Counter Terrorism Service (a “mandat” is a 4-month tour of duty). French Air Force assets are not based inside Iraq but in Jordan and the UAE.

The French military doesn't communicate much on special operations (although it did regarding the TF Sabre in the Sahel region) but press reports suggested that operators present in Kurdish areas in Syria had to leave hastily when the US retreated there. Nothing on potential operations within Iraq.

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According to one US diplomat, there are 16 countries currently part of the coalition providing support and training to the Iraqi military, although he did not provide a detailed list of these countries.

if U.S. forces leave Iraq it means almost certainly that the other 16 members of the military coalition that is still helping the Iraqis fight ISIS in training the Iraqi Army will also leave.

A bit more googling found an older (2016) article listing 16 countries... the list includes Iran and Russia though, so maybe all of them leaving is a bit of exaggeration... Some excerpts for the NATO & Western countries (omitting aircraft info):

  • Up to 350 British soldiers and advisers are deployed in Iraq, centred in Erbil and Nineveh. Their role is limited to training as well as logistical and aerial support for the Iraqi army and Kurdish Peshmerga forces.

  • Around 200 Australian special forces are present in the Kurdistan region, overseeing training, support and electronic surveillance of IS.

  • Belgium deploys 120 soldiers and trainers in a camp near the Jordanian border with Iraq as well as in Kurdistan. They provide support and surveillance to anti-IS operations in northern Iraq.

  • Up to 700 Canadian military personnel are present in Baghdad and Erbil, providing training, support and reconnaissance.

  • Denmark: The Scandinavian nation has 140 military mostly non-combat personnel in advisory and training capacities. They are present in a small base shared with the Peshmerga southwest of Erbil.

  • Around 500 French military personnel are present in Iraq as part of the special forces unit. Most of them are serving in a support capacity, including analysts working with images provided by fifteen French reconnaissance planes operating over Iraq and Syria.

  • Berlin maintains 150 military personnel mostly officers, part of a newly formed European anti-terror unit, based between Baghdad and Erbil. Germany also runs a training camp for Kurdish volunteers and fighters, with focus on programmes related to use of European weapons supplied to Iraq, mostly Kurdistan. Germany is part of the international coalition.

  • Rome dispatched 450 military personnel to Iraq amid warnings of the collapse of a dam in Mosul.

  • Around 150 Dutch soldiers are training Iraqi soldiers in northern Iraq.

  • Turkey has contributed nearly 600 troops, tasked with training Kurdish forces and Mosul tribes to fight IS and force it out of the city, as well as protecting borders from PKK infiltration. It has weapons and armoured vehicles to defend its camp in Bashiqa, 30 kilometres northeast of Mosul.

  • Sweden: Forty advisers working with the army.

  • Norway: Unknown number of trainers in Baghdad.

  • Spain: A few dozen trainers working with the Iraqi army and local police in Baghdad and northern Iraq.

I don't know how up-to-date that list is for 2020.

Of note however is that NATO has an official mission in Iraq; from its official page:

At the Brussels Summit in July 2018, NATO leaders agreed to launch NATO Mission Iraq (NMI), on the request of Iraq.

NMI is a non-combat training and capacity-building mission, conducted with full respect of Iraq's sovereignty and territorial integrity.

It was established in Baghdad in October 2018 and involves around 500 trainers, advisors and supporting personnel from Allied and partner countries, including Australia, Sweden and Finland.

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They are not significant. What they may be talking about is PMCs and other no state actors.

They are not "coalition" bases, just Iraqi bases where contractors are housed. An example

https://www.google.com/amp/s/www.nytimes.com/2019/12/27/us/politics/american-rocket-attack-iraq.amp.html

There is probably not enough coalition troops in Iraq to require a base, a news search turns up little. However PMCs use Iraqi bases and are there in large numbers up to 180k in the past but now less.

https://www.globalpolicy.org/pmscs/50154-iraq.html

As of the fourth quarter of FY2018, there were 6,318 DOD contractor personnel in Iraq and Syria (see Table 3). Approximately 49% of DOD’s reported individual contractors were U.S. citizens (3,086), approximately 38% were third-country nationals (2,405); and roughly 13% were local/host-country nationals.16 As of FY2018, CENTCOM has not resumed reporting data on DOD-funded private security personnel in Iraq.

For comparison, Wikipedia says Daesh has approximately 15000 fighters in Iraq so the DOD contractors are approximately 1/3 the strength.

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