ABB made the admission in its latest annual report and filing to the US Securities and Exchange Commission under US accounting rules. The group plans to list on the stock market in the near future.
An electrical equipment company, ABB bought Combustion Engineering in 1990 from which the claims arise.
A spokesman for the company confirmed the company is subject to pending asbestos litigation, but was unable to disclose the size of insurance coverage the company has.
ABB had maintained a $590m (£411m) reserve to cover what it estimates will be the cost of settling the cases and about $160m (£111m) for probable insurance recoveries.
Estimating the size of reserves necessary to cover future liabilities is fraught with difficulty as asbestosis can take up to 40 years to appear.
Asbestos-related liabilities recently spelled trouble for UK insurer Chester Street Insurance Holdings. In January, directors declared the company, which covered many shipyards and factories where workers were exposed to asbestos, insolvent.
PricewaterhouseCoopers was appointed provisional liquidator and helped implement a scheme of arrangement, which was unanimously accepted by creditors.
The firm moved swiftly to make an initial 5% payment to Chester Street?s creditors.
But on Saturday more than 1,000 protestors marched through Clydebank in Scotland demanding more compensation than the 5% so far delivered.
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