The Nikkei index in Tokyo began to fall 3.5 percent shortly after opening. In Hong Kong, the Hang Seng Index opened a decline of 2.1%.
The stock exchanges in Shanghai and Shenzhen, which on a smaller scale follow the other markets in the world, also fell, though not so much. The first fell 1.2 percent, while the decline in Shenzhen was 1.1 percent.
The top index of one of Asia's top stock exchanges has come out on Tuesday. Investors in Asia appear to have become wary after Wall Street fell on Wall Street on Monday because of turmoil over demand in the technology sector.
On the New York Stock Exchange, the Dow Jones Index fell 2.3 percent on Monday, while the broader S & P 500 index fell 2 percent.
The Nasdaq Exchange, rich in technology, fell even more on a day when Apple fell 5%, while Amazon fell 4.4%. The main index closed down 2.8 percent when the Nasdaq closed Monday.