It isn’t just that there is too much oil sloshing around the world. All of a sudden, there are fears of too little demand for the stuff too.  Oil prices continued to tumble Thursday, with Brent crude, the international benchmark, falling 5% to its lowest levels in more than a year. The U.S. benchmark, West Texas Intermediate, settled at $45.88 a barrel, a 17-month low, and is down 40% since a high in October.

Signs are mounting that oil consumption in China, India and other economies across emerging Asia—the source of two-thirds of global oil-demand growth—is slowing, and uncertainty around the U.S.-China trade spat is further clouding the outlook. Problems in the eurozone, including recent protests in France, could also crimp oil purchases, analysts say.  “The more we look at demand numbers, the more we see that something fishy is going on,” said Eugene Lindell, senior oil-market analyst at Vienna-based consulting firm JBC Energy.

Mr. Lindell recently cut his forecast for global oil-demand growth next year to 888,000 barrels a day, which would be the slowest increase since 2011. Other analysts see higher, but still slowing, growth next year. Since the financial crisis, demand has grown on average around 1.5 million barrels a day each year.  Adding to the jitters, stock markets are in correction territory and economic readings from around the world have come in below expectations.

Given the economic anxiety, Amrita Sen, co-founder and head of research at London-based consulting firm Energy Aspects, recently lowered her demand-growth estimate for next year to 1 million barrels a day. Energy Aspects cut its price forecast for U.S. crude next year to $66 a barrel on average, down from $72 earlier.