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The Wikipedia article suggests that private civilian flights are allowed, but I'm in Canada, and too far away to test that myself.
Huge airport for a rather poor region in Paraguay. Big radar station, aparently not in use anymore. Very old equipment inside. Barnstead Puromatic for water purity measurements??? Why do you need that on a lost airport, unless it was planned to be used for something else. 3800meters long and 60meters wide indicates that it can be used for large mililtary planes. Funded by the US in the early 80s for purpose of regional domination, like they do in so many other countries. Currently being guarded by paraguayan military, so it's kinda hard to get on to.