Many pieces have been written, recently, discussing the end of US hegemony. Some frame this in terms of internal US issues — US debt, or the US looking inwards and ceasing its concern with world affairs. More often commentators suggest that China will overtake the US in terms of the size of its economy, and perhaps in terms of influence in Africa or even South America.
Most of these discussions seem pretty confused to me. The US hasn't been the hegemon for terribly long —only since 1990 has its power been unchallenged. It shouldn't be surprising that some other power might rise to take it on, but the emergence of a rival does not necessarily imply the victory of that rival —hegemons often see off several challengers before they go down.
Next, the idea of China as a rival to US hegemony seems well wide of the mark. Most discussions framed in those terms appear set up for a bipolar world, as when the US faced the Soviet Union. With the Soviet Union gone, China is expected to slot in. But China does not remotely have the global ambitions of the Soviet Union, nor any ideology of world domination / conversion of the Soviet type. China regards itself as constituting the whole of the important world. It has regional interests, in the immediate theatre around China. And whereas the Soviet military emerged with confidence from mighty victory against the Nazis, the Chinese military is acutely aware of its limitations — it has been notably unsuccessful since the Korean War, and has struggled even to unite China or settle its border disputes favourably, let alone being placed to pursue broader ambitions (if it had any).
Furthermore, Chinese economic development will not be linear. As with the Japanese, at some point Chinese workers will cease being grateful that they are not peasants eating rice, and thus willing to work long hours for low pay, and will instead want to be paid and consume. In Japan, this transition in the 1990s was associated with a reversal of the relative unit labour cost trend of previous decades, with US unit labour costs re-overtaking Japanese. Something similar can be expected in respect of China, in due course.
Besides all this, there is a much more urgent and explicit threat to US hegemony: the Single European State. In 2011 the Eurozone had a GDP of US$13.1 trillion, versus the US GDP of US$15.1 trillion. Similarly, unlike China, Eurozone GDP per capita, wealth per capita, and capital stock are all comparable to that of the US. We thus don't need to wait until 2050 for another economy to be around the same size and wealth as the US' — if the euro does not collapse and the Eurozone achieves its explicit ambition of political union, there will be a coherent confederation similar in size to the US well before the end of this decade. Furthermore, unlike China, the Single European State has an explicit ambition to serve as a counterweight to the US in world affairs — that has, for example, been an explicit French understanding of the European community for decades.
The US would, perhaps, prefer to think of the Single European State as a partner or ally, rather than as a challenger — at least in public. But then the US preferred to describe the British Empire as a partner, also — and that didn't prevent the US from dispatching it when it had the opportunity. (I say that without rancour — that was only right and proper, the way one would expect any serious great power to behave.)
The Single European State would share many political assumptions with the US, in respect of democracy, human rights and so on. But it would not be perfectly aligned in these areas, and would have divergent interests in terms of priorities for the security of energy supplies, the balance of risk associated with certain military ventures (e.g. ventures where taking the risk of violence spilling over into neighbouring states might seem worthwhile to the US, but not to the Single European State, when those neighbouring states are far from the US but on the Single European State's doorstep), and in various commercial or financial areas. The Single European State would be much less susceptible to US pressure or menace than would many other countries. We could expect the Single European State to challenge the US even more than the EU already does in fora such as the WTO or the UN.
Many US observers, or those from other parts of the world such as Australia, continue with an obsolete picture of "Europe" as an entity that includes Britain (irrelevant already, and will be even more so as the Single European State intensifies) and as a fractious set of constantly shifting interests. They imagine that it would be welcome if only Europe would "step up to the plate" in terms of its responsibility for world affairs, raising military budgets and sending more soldiers to difficult regions. But the Single European State will not be shy and will not operate with US shibboleths. It may not raise its military spending to US levels, but it will not see the point of doing so. The burden of high military expenditure will weigh down the US, relative to the Single European State, over time.
It is easy, and wrong, to assume from current travails that the Single European State will necessarily be damaged in the long-term. It may be destroyed, if there is a disorderly collapse of the Eurozone. But if that does not happen, it will be immeasurably strengthened, and a new Great Power will stalk the Earth.
I, for one, will welcome it.