IN FINANCE, things that grow very fast have an irksome tendency to blow up. American subprime mortgages prior to 2008, southern European sovereign debt in the run-up to 2010 and Japanese banks in the 1980s are but recent examples. So it is worrying that bank lending in emerging markets has ballooned in recent years, from about 77% of GDP in 2007 to 128% at the beginning of this year, according to JPMorgan Chase, a rich-world bank (see chart). That 51-percentage-point jump dwarfs the mere 20-point rise in credit in the rich world in 2002-07.

Now that the economic prospects of emerging markets have dimmed, banks from Shanghai to São Paulo are in the spotlight. Trouble in such places would once barely have registered in global financial circles. In 1990 only three of the world’s 100 biggest lenders by assets were in developing countries. Now the world’s four biggest banks are in China, and the fifth-biggest, HSBC, does much of its business from Hong Kong. More than a third of the world’s biggest banks have their headquarters in emerging markets, and plenty of rich-country firms (such as Standard Chartered, based in London, or BBVA, a Spanish bank) operate there.

Banks that have expanded at such a rapid clip in the past have typically issued more than a few dud loans along the way, and stretched their balance-sheets beyond comfort. Happily, regulators have learned the lessons of past crises in most emerging markets, so systemic turmoil is unlikely. It is the banks’ ability to finance a return to rapid economic growth that is in doubt.

The Institute of International Finance, a trade group, predicts that 2015 will be the first year of net capital outflows from emerging markets since 1988. The good news is that emerging-market banks have little trouble funding themselves. Many emerging economies, especially in Asia, have high savings rates. That leaves most lenders with more deposits than loans, even though loans have been growing faster of late. Rich-country banks, in contrast, have to make up for a shortage of deposits by tapping fickle wholesale markets, leaving them more vulnerable to sudden changes in sentiment.

If liquidity is not an issue, solvency may be. Banks in emerging markets tend to be profitable: the listed ones generated net income of $563 billion last year, up from $94 billion a decade ago.

Unlike their Western peers, few have investment-banking arms, which have attracted profit-sapping regulation and fines from watchdogs.

But profits can also be wiped out by dud loans, which must eventually be written off. Though lending to consumers is growing, emerging-market banks lend mainly to companies.

Unfortunately, troubled industries such as property (a Chinese speciality), infrastructure development (India) and commodities (Brazil, Chile and Nigeria, among others) feature prominently in loan books. In India non-performing or restructured loans now account for more than 14% of the assets of public banks, which control three-quarters of the market. In China they are low but growing fast.

Currency mismatches are another concern. The prospect of higher interest rates in America, plus declining commodity prices tied to a slowdown in the Chinese economy, has pushed most emerging-market currencies down relative to the dollar. Collectively, they have fallen by around 30% against the greenback since early 2013.

That can affect banks directly, if they have borrowed dollars to finance loans in local currencies—a trick that is very profitable when currencies are steady. Regulators in Asia, whose banks were caught in this trap in 1997, now monitor banks’ exposure to currency movements. But their counterparts in Nigeria and Turkey, in particular, have not been so exacting.

Even if banks have avoided currency mismatches, their customers are not always so prudent.

Low interest rates in America have sent some developing countries on a dollar-denominated borrowing spree: external corporate debt in emerging markets amounts to $1.3 trillion, according to the Bank for International Settlements. Dollar-denominated loans make up 25% of corporate lending in Russia, perhaps 30% in Turkey and probably even more in Nigeria (the data are fuzzy). Firms will struggle to repay those dollars with devalued roubles or naira.

Commodity producers would normally be immune to this problem, since their income is in dollars, but the plunge in commodity prices has ensnared them, too.

Inflation, which has been stoked by devaluations in several emerging markets, will also cause problems. Rising prices sap consumers’ purchasing power and prompt rises in interest rates (they are in double digits in Brazil and Russia). That can make it hard for borrowers to service their debts. The share of household income going to debt service seems to be rising in Brazil, China and Turkey, among other places.

There is little sign yet that bad debts will reach catastrophic levels. But unless banks face up to them, their long-term consequences could nonetheless be grim. Lenders often try to sweep their problems under the carpet. One common strategy is to “extend and pretend”—giving companies with little prospect of paying back a loan years of forbearance. This ties up scarce capital in zombie firms, which can lead to years or even decades—in the case of Japan—of subpar growth.

There are signs that emerging-market banks are hiding losses in this way. Chinese ones, for example, put non-performing-loans at just 1.6% of assets, less than half the global average.

Investors plainly don’t believe them: their share prices imply dud loans of more than 8%, according to Barclays. By the same token, international banks that do business across emerging markets often disclose far higher levels of distressed loans than local banks.

Emerging-market banks are no longer the undersized tiddlers of global finance. The way they are run matters more than ever. Their balance-sheets are healthy enough to weather the aftermath of the credit bender they initiated. But whether they bounce back or limp along depends on how quickly they admit their failings.