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You can submit flight delays claims or ask for a flight cancellation refund if the case has happened not more than 3 years ago. However, some airlines set other limits. For example, in some companies claiming for delayed flights is allowed only for 2 years after the delay/cancellation or within the whole 6 years after such case has happened. It all depends on the airline and on the legislation of the country of the claim.
If you hesitate whether you are eligible to claim delayed flight or get compensation for cancelled flight, you can always contact one of the companies that can help you solve your particular issue. Most of the companies offer you to check your case online in a few minutes, and if you have the right to get the compensation you can hire professionals to deal with it.