Whether these calculations figured in the arms negotiations is hard to say, in part because the government insists that the arms being negotiated — antitank missiles, rocket launchers and portable rockets capable of bringing down aircraft, among others — were never delivered. Technically, at least, Chinese arms vendors are not required to seek permission before talking about deals with foreign customers.

On the other hand, some of the companies involved in negotiations with Colonel Qaddafi’s government have a track record of skirting sanctions, American officials say. The United States has repeatedly cited two of the firms, the China North Industries Corporation and the China National Precision Machinery Import-Export Corporation, for selling missile technology and other equipment to Iran that it says violate international sanctions.

Chinese officials have argued that the Americans rely on incorrect information or too-sweeping definitions of prohibited weapons components.

More broadly, China’s record on enforcing international sanctions remains weak, many experts say. For example, the latest United Nations report on the enforcement of sanctions against North Korea, issued in May, faults China for failing to intercept suspected shipments of ballistic-missile items on North Korean cargo planes that land there en route to Iran. After vigorous protests by the Chinese, the report identified China only as “a neighboring third country.”

Chinese companies were major suppliers in the past decade of small arms and ammunition to Sudan, where they fueled the conflict in Darfur despite a United Nations prohibition. Similar charges have been leveled in wars in Congo and other African nations. Chinese officials say they have no control over arms once they reach their destination.

In theory, the violations should never occur to begin with. A government agency issues arms-export licenses in consultation with China’s Defense Ministry and its Foreign Affairs Ministry. The Defense Ministry is supposed to advise whether a weapon or technology is suited to sell to others. The Foreign Affairs Ministry advises whether they should be sold at all.

But in the Chinese government, as in Chinese life, personal relationships carry huge weight. And it is widely believed by outside experts that the fraternal ties between arms makers and the military, which owned many of them before weapons-making was hived off in the 1990s, overwhelm the diplomats’ say in the process. “The state-owned enterprises have a lot more leeway with regard to whom they can trade with,” said Stephanie Lieggi, a senior researcher and an expert on China’s arms industry at the Monterey Institute of International Studies in California.