Shoprite Holdings Ltd. sold more Guinness stout at its 11 stores in Angola and Nigeria last year than at home in South Africa, where it has 10 times as many outlets.

But Africa’s biggest retailer is also contending with an Islamic insurgency in Nigeria, where Boko Haram militants have staged attacks near its shops—and the effects of wilting currencies both there and in Angola.

The challenges are increasingly common ones for Africa’s largest companies, serving customers embattled by insecurity and economic turmoil.

“These are still relatively high-growth countries, and these experiences can be a long-term gain,” said Corneleo Keevy of Ashburton Investments, an arm of Johannesburg-based banking group FirstRand. “Expanding in Africa isn’t an overnight play.”

Anemic growth in the continent’s most advanced economy, South Africa, and instability in its largest, Nigeria, have buffeted the continent’s biggest companies, complicating efforts to burrow into the global economy’s newest frontier before their foreign competitors.

Their home market, South Africa, is racked by joblessness and power blackouts. The economy that gave rise to major banks and telecom firms like Standard Bank Ltd. and MTN Group is now growing less than 2% annually.

They and their peers have pinned their hopes on Africa’s ascendant giant, Nigeria. But that country of some 170 million people is now wrestling with a tanking currency and Boko Haram. These are serious obstacles to its growth in the immediate future that the newly elected government of Muhammadu Buhari will have to deal with after his swearing in.

The troubles in Africa’s two top economies have left executives juggling cost-cutting and aggressive marketing pushes there, while plotting to boost their business in smaller but promising African countries like Angola and Kenya.

“These are risky markets but it would be riskier not to be there,” said Konrad Reuss, Standard & Poor’s Ratings Services’ managing director for sub-Saharan Africa. He acknowledges, though, that “there might be less money to go around for a while.”

Indeed, analysts say companies determined to tap Africa’s growing middle classes cannot ignore Nigeria.

“There’ve been a lot of negatives but these hopefully are short-term,” Shoprite Chief Executive Whitey Basson told South Africa’s Sunday Times newspaper in March. “We really treat it as something we must cope with and learn how to deal with.”

And it will take decades before people in most of Africa amass the spending power of South Africans, so both countries remain central to African corporate strategy.

But the current fragilities of these two African giants show that setting up shop in the rest of the continent is critical in hedging bets. Africa as a whole is growing at 5%, not far behind other billion-person emerging economies, China and India.

Nigeria overtook South Africa last year to become the continent’s biggest economy, but its dependence on oil has sent its currency tanking as global oil prices have dropped. Boko Haram’s attacks in the northeast mean a swath of the country is a no-go zone.

The Nigerian experience of South Africa’s MTN Group shows both the risks and rewards of these continental forays. Revenue at the continent’s biggest telecom company shrank 3.9% last year. In Nigeria, MTN’s biggest market and where it hopes to aggressively boost income, revenue only rose 3.4%, well below expectations. Nigeria had been a key source of profits for MTN in previous years, doing so well that the local competition authority had to put restrictions on it because it was deemed a “dominant player,” controlling half the market, in 2013.

For now, analysts say MTN and other South African companies could struggle to pull profits out of Nigeria while the naira lingers at record lows and the central bank restricts access to U.S. dollars.

For MTN, weathering the storm means expanding across Africa and the Middle East, including in some sanctioned states like Syria, Iran and Sudan.

Sim Tshabalala, co-chief executive of Standard Bank Group, the continent’s biggest lender by assets, sees opportunities in the rest of the continent. Standard Bank Ltd. recently reported that almost a third of its revenue in 2014 came from sub-Saharan Africa excluding South Africa—up 41% from the previous year.

“As the continent gets wealthier and enters the middle class, it needs banking services,” Mr. Tshabalala said in an interview, singling out East Africa and especially Kenya as big sources of future revenue. The region was the fastest-growing for Standard Bank in 2014, he said.

Still, illustrating the bank’s current conundrum, South Africa in the short term remains crucial: “Banking penetration and financial deepening in those markets is shallow compared with South Africa,” he said, meaning the proportion of Africans that use banks is still small.

Smaller South African firms are also embarking on pan-African adventures to shield their bottom lines. Packaging company Nampak Ltd. recently purchased a $300 million can factory in Nigeria, and is finishing construction on a second $180 million can factory in Angola.

“Some impact on the consumer’s pocket is probably unavoidable,” as a result of the oil-price and currency drops, Nampak Chief Executive André de Ruyter said. But in the long term, he said, his firm’s future depends on growth outside South Africa, where power outages and labor strikes have crimped economic growth.

“We cannot rely on GDP growth here to give us the volume growth we need to drive increased profitability,” he said.