Workers exposed to asbestos have been seeking damages
Insurers have appealed against the decision to allow legislation which gives victims of an asbestos-related illness the right to claim damages.
Last week, a judge rejected a bid to invalidate The Damages (Asbestos-related Conditions)(Scotland) Act which came into force last year.
It allows sufferers of pleural plaques, a benign scarring of the lungs, to make compensation claims.
Aviva, AXA, RSA and Zurich believe the Scottish Parliament act is "flawed".
The law overturned a House of Lords ruling which said damages could not be claimed for the illness, which is not classed as a disease and has no symptoms.
Although pleural plaques does not cause or develop into a more serious asbestos-related condition, it does signify an increased risk of developing mesothelioma because of exposure to asbestos.
Nick Starling, director of general insurance and health with the Association of British Insurers, said: "After careful consideration and legal advice, insurers consider that there are good grounds for this appeal.
"Insurers have not taken this decision lightly, and it reflects their strong view that The Damages Act is fundamentally flawed as it ignores overwhelming medical evidence that plaques are symptomless, and the well-established legal principle that compensation is payable only when there are physical symptoms."
The ABI said the appeal would not affect insurers commitment to pay compensation to people with asbestos-related diseases, such as mesothelioma.