Thanks for posting your buying needs on Ariba Discovery. There are over 700,000 suppliers on Ariba Discovery, and a large portion of them are outside of the United States. The number of responses you will get to your posting depends on a couple of factors, such as the items or countries you're looking for. Sometimes, it's easier to find matching suppliers if you don't expect a single supplier to cover all territories or products. That way, you might be able to find multiple suppliers who can cover part of what you're looking for.
Here's a case study that covers how US-based Abercrombie & Fitch discovered Germany-based EASI on Ariba Discovery: http://exchange.ariba.com/docs/DOC-1967 . And this one gives you more insights on how Jotun Paints (a Norwegian company) discovered packaging suppliers for its UK business: http://exchange.ariba.com/docs/DOC-2312
Feel free to reach out with any further questions.