March31, 2006: On March 30, 2006, the U.S. and Russian navies finished a PASSEX (passage exercise) off the coast of Guam. This sort of thing is done to enhance cooperation between two navies. Two American cruisers, the USS Cowpens and the USS Chosin, operated with the Russian destroyer Marshal Shaposhnikov; the tank landing ship BDK-11; the oiler Pechenga; and the tug SB-522.

What's odd about this is that it's tagged as a "humanitarian assistance and disaster relief" exercise, as well as a PASSEX. None of the official news releases described the humanitarian and disaster relief part of it, but it would be hard to do in conjunction with a PASSEX.
Apparently Marshall Shaposhnikov is one of only two Udaloy Class ships that seem to make it to sea regularly; the Russians have been experiencing a severe shortage of spare parts for their gas turbines. The Soviets put the factory for these engines in Ukraine, and Ukraine is now charging serious bucks for spares. The Russians are building their own plant to ease the problem.
Note the presence of the tug. It's always been standard practice when units of the Russian fleet deployed, and has on occasion proven useful.

Actually, even during the Cold War there were occasions on which US and Soviet warships participated in exercises together. Usually these were being staged by some Third World country that invited both, like India, Pakistan, or Ethiopia (until Haile Selassie was ousted).