So far, some insurers are including coverage for basic problems in their general liability offerings, but most are asking customers who want significant coverage to pay for separate packages.

High-tech companies are the most likely to buy cyberinsurance in case their services or products fail their customers. But the insurance industry wants all companies with any sort of Internet connection to take out cyberinsurance, and the federal government is particularly hopeful that companies in industries traditionally considered utilities will buy it.

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