Adm. Mike Mullen, left, chairman of the Joint Chiefs of Staff, shakes hands with Gen. Chen Bingde, right, chief of the General Staff of the Chinese People's Liberation Army, before their meeting at the Bayi Building on July 11, 2011 in Beijing, China. (Photo: Alexander F. Yuan - Getty Images)

Military relations between the U.S. and China are a glaring weak spot in bilateral ties, something Admiral Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, said he hoped to improve during a trip to China this week. His visit was the first by the highest-ranking military officer in the U.S. since Mullen’s predecessor Gen. Peter Pace went to China in March 2007. The Chinese government severed military contacts with the U.S. in January 2010 after President Obama approved the sale of a $6.4 billion arms package to Taiwan, the independently governed island that China considers part of its territory. Those ties only resumed in late 2010, as China smoothed the path for President Hu Jintao’s state visit to Washington this January. In May Gen. Chen Bingde, Mullen’s counterpart, visited Washington in May, the first visit by the People’s Liberation Army’s chief of general staff since 2004.

Speaking to reporters in Beijing on Monday, both Chen and Mullen emphasized some recent advancements, saying the two countries would hold joint anti-piracy exercises later this year in the Gulf of Aden, off Somalia, and meet in Hawaii to discuss operational safety issues. But the two also acknowledged that serious obstacles remain. Chen complained about U.S. naval exercises planned with Vietnam and the Philippines, two countries China has been sparing with in recent months over rival territorial claims in the South China Sea. The U.S. says it wants to protect the freedom of navigation in the region, and wants to see a peaceful resolution to the disputes. China accuses the U.S. of meddling in a regional issue, and Chen called the timing of the military exercises “inappropriate.”

Chen also criticized U.S. surveillance of China, saying reconnaissance drones have flown within 16 miles of Chinese territory. Surveillance flights have been a flash point in the past, and in April 2001 a U.S. EP-3 spy plane collided with a Chinese fighter sent to intercept it, killing the Chinese pilot and forcing the U.S. crew to land on China’s Hainan Island. As regional militaries expand their activities in the Western Pacific, with warships and aircraft jostling in disputed areas like the South China Sea, the likelihood of incidents increases. That raises the importance of military ties, so that provocation is kept at a minimum and accidents don’t develop into outright conflict. Unlike during the Cold War, when the U.S. and the Soviet Union agreed to a set of rules to manage incidents on the high seas, the U.S. and China have yet to come to a similar agreement. China doesn’t recognize the right of U.S. naval vessels to operate within its 200-mile exclusive economic zone and it also worries that an agreement on incidents at sea would smack of Cold War rivalry, which China hopes to avoid with the much larger U.S. military.

The U.S. spends about six times what China does on national defense, a point that Chen criticized in his press conference with Mullen. He said that after seeing the advance state of the American military on his visit in May, he was left thinking that U.S. priorities were misplaced at a time when the country should be worried about the state of its economy. “I know U.S. is still recovering from financial crisis, still have some difficulties in its economy, while at the same – while at the – again, in such circumstances, U.S. still spending so much money on the military. And isn’t it placing too much pressure on its – on the taxpayers?” Chen said. “If U.S. could reduce a bit military spending to spend more on the improvement of livelihood of the American people and also do more good things for world people, wouldn’t it – wouldn’t it be a better scenario?”

That gap in size between the two militaries is one of the biggest obstacles to improving ties. Over the past decade China has rapidly expanded its military capability, increasing spending by an annual average of about 15% since 2000. While the U.S. has a vastly stronger fighting force, it clearly worries about China’s growing might. So it pushes for closer links and greater transparency, which the PLA has been slow to welcome. During this trip Mullen visited the headquarters of China’s Second Artillery Corps, which operates the country’s nuclear missiles, and checked out SU-27 fighter jets on a visit to an air base in Shandong province in east China. But the U.S. can be expected to push for even more openness from China in the future, and China will likely resist. “Transparency is good if you’re a strong power, and you want to deter other countries,” says Ian Storey, a fellow at the Institute of Southeast Asian Studies in Singapore. “If you’re a weaker country, transparency simply exposes those weakness. That’s one reason why the PLA has not embraced transparency.”