Does anyone know of an international postdoctoral association? The number of postdocs is increasing worldwide. Because of their technical expertise and dedication, postdocs are rapidly becoming the backbone of most large science laboratories. 

I am aware of institutional associations for postdocs, which are venues for networking, exchange of ideas, solving problems. At the local scale. 
Examples:

http://www.nationalpostdoc.org 

http://jhpda2.jhu.edu

https://uwpa.wisc.edu

However many postdocs move from their original departments, and became international. And it is my impression that similar challenges are faced by postdocs around the world, and it is quite hard finding out how things are going with colleagues abroad. Especially on delicate matters, via cold emails. 

Please, would anyone be aware of some international association where postdoctoral fellows worldwide could meet, and discuss their difficulties and experience?
It's a great idea Scientist/Tommi but there's none yet that I'm aware of.  

A lot of issues are common to different countries, but there are many important differences too. A good reason to look up your national/sector/discipline association, and a possible roadblock to the establishment of an international group.

In Australia it's the EMCR Forum*. They recently asked about similar international groups that advocate for and represent early and mid-career researchers and got a few bites: https://twitter.com/EMCRForum/status/950530138491400197 


full disclosure: I am deputy chair of the EMCR Forum in 2018