So it looks rather worrying from a Western point of view that the group has agreed to expand and that India, Pakistan and Iran are all keen to join: the rise of a kind of China-led NATO to which even America's friends, such as India and Pakistan, seem drawn. Yet that is to misunderstand the sort of organisation the SCO aspires to be. It does indeed pose a challenge to the American-led world order, but a much more subtle one.
On September 11th and 12th the SCO held its 14th annual summit in Dushanbe, Tajikistan's capital. It agreed to adopt procedures for expansion, first for those countries that are already observers. India and Pakistan are likely to join in the next year. Iran is at present disqualified because it is under UN sanctions. Another observer, Mongolia, is a democracy and has long had qualms about joining what looks like a club for authoritarians. Afghanistan, the final observer, has other priorities.
The SCO summit came hot on the heels of one held by NATO, in Wales. This gave columnists in China and Russia the chance to tut-tut about the "20th-century" or "cold war" or "confrontational" mentality that animates NATO, and to boast about what makes the SCO different from what Russia's foreign minister, Sergei Lavrov, has called such "relics of a past era", with the rigid discipline imposed by particular blocs of countries.
In August the SCO held its largest joint military exercises yet, an anti-terrorist drill in Inner Mongolia in China involving more than 7,000 personnel. The SCO's boosters, however, insist it is not an alliance, like NATO, but a "partnership", with no adversary in mind. That is not entirely true. It has always been explicitly directed against three enemies, even if they are only abstract nouns: the "three evil forces" of terrorism, separatism and extremism. China, in Xinjiang; Russia, in Chechnya; the Central Asian members, in the Ferghana Valley and on their borders with Afghanistan. All SCO members face a threat from Islamist extremism.
Hence the plea in Dushanbe from Xi Jinping, China's president, that the SCO should "focus on combating religion-involved extremism and internet terrorism".
China's problems with violent extremism from ethnic-Uighur Muslims in Xinjiang have worsened recently.
Uighur militants have committed terrorist attacks in Xinjiang and other parts of China. They have also been fighting for jihadist groups elsewhere--in the tribal areas of Pakistan, for example. And reports suggest some have joined Islamic State (IS) in Iraq and Syria. This month four Uighurs with alleged IS links were detained on the Indonesian island of Sulawesi.
These men had left China by way of South-East Asia. One of China's successes in Central Asia in recent years has been to secure the co-operation of local authorities in deporting illegal migrants--meaning mainly Uighurs with a grudge--so more are finding their way out through Laos and Thailand.
That success, however, is probably more the result of China's growing presence and commercial clout in the region, and the rendition agreements they have bought, rather than a tribute to the influence of the SCO itself. The same goes for the economic goals China has set the SCO. The countries it covers are on the "New Silk Road" Mr Xi advertises. But it is bilateral deals that will build the dream, not communiqués from an SCO summit.
Viewed like this, not as a regional security bloc but as a rather ineffectual effort at combating cross-border terrorism and boosting other links, the SCO seem less threatening. Its appeal to India and Pakistan also seems more obvious, especially as NATO's withdrawal from Afghanistan opens up new uncertainties in the region. Membership incurs few costs and may have some benefits. India, for instance, is courted both by China--Mr Xi paid a much-trumpeted visit this week--and America. SCO membership would be a useful way for India to flaunt its independent foreign policy and its refusal to be drawn into an anti-China bloc.
For China, however, and even more so Russia, the accession of India and Pakistan would be a mixed blessing. The SCO would look less like a self-absorbed club focused on Central Asia, and it would gain real global heft. However, as other regional groupings have found, expansion would inevitably be at the expense of the SCO's cohesion. India, even under the leadership of a strongman like Narendra Modi, would not sit comfortably in an authoritarian club. The SCO would be able to do even less than it has so far.
In fact, even Russia and China seem unsure about how important they want the SCO to be. Four SCO members also belong to the Russian-led Collective Security Treaty Organisation. Russia is also hoping its Eurasian Union with Belarus and Kazakhstan can expand. And China has started lavishing attention on another organisation, the leadenly named Conference on Interaction and Confidence-Building Measures in Asia, or CICA.
But to note the potential conflicts among the different multilateral organisations China is promoting may be to miss the point. America's leading role in Asia is based on a number of bilateral security treaties and a plethora of inclusive multilateral institutions, all open to Chinese membership. China itself is building all sorts of institutions: the SCO, CICA, the "BRICS" (grouping China with Brazil, Russia, India and South Africa), a Trilateral Commission (at present languishing) with South Korea and Japan and a Regional Comprehensive Economic Partnership.
Their shared characteristics are that China has a big and sometimes dominant role and that the United States is not a member--and indeed was rebuffed when it sought to join the SCO as an observer. China is not just challenging the existing world order. Slowly, messily and, apparently with no clear end in view, it is building a new one.