Upgrade the os

• macOS High Sierra - Technical Specifications - MacBook Air (Late 2010 or newer)
• macOS Mojave - Technical Specifications- MacBook Air (Mid 2012 or newer)

How to get old versions of macOS

Back up your data, check your applications for compatibility, and click on High Sierra. It can't be upgraded past there.

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WEN2000 Said:

"Upgrade the os: I bought one old MacBook air 13 mid 2011. I try to upgrade the os, but it always said that the os is too old. How can I do?"

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Upgrading to Big Sur:

It cannot have the latest version of macOS (Big Sur), as its hardware does no meet the system requirements.

See Here: macOS Big Sur - Technical Specifications - Apple Support