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Yes, military veterans who become disabled during their service can collect disability benefits from the Social Security Administration (SSA) and U.S. Department of Veterans Affairs (VA) disability compensation at the same time. And many do. More than 950,000 former service members received Social Security Disability Insurance (SSDI) in 2016, according to the most recent data available.
The two federal agencies have different processes and rules for determining eligibility and setting payments, and getting VA disability benefits doesn't necessarily mean you'll qualify for SSDI. But if you've received a 100 percent permanent and total (P&T) disability rating from the VA, Social Security can expedite processing of your SSDI application.

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How SSDI and VA disability compensation differ
Qualification
You may qualify for VA disability compensation if you were injured or developed a physical or mental illness during your service or if a preexisting condition got worse as the result of your time in the military.
The SSA is not concerned with how you became ill or injured; rather, qualification for SSDI is based on your work history: You must have spent a certain period of time in “covered” employment — meaning jobs or self-employment in which you paid Social Security taxes.
Medical eligibility
Social Security bases eligibility for disability benefits on whether your condition is severe enough to prevent you from doing most paid work for at least a year or is likely to result in your death. By the SSA's lights, you are either disabled or you're not.
By contrast, the VA rates disabilities on a percentage scale, based on how much it thinks a particular condition affects your health and ability to function. The agency assigns different percentages to various injuries — for example, how much of a leg was amputated as the result of an injury, or which fingers.