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I see that you are having issues listening to your Apple Music content when you are offline. As described in this support article,
Add and download music, shows, and movies from the Apple Music catalog
If you want to listen to content offline, here are the steps to follow:
If you subscribe to Apple Music, you can add songs, albums, playlists, shows, and movies to your Library from anywhere in Apple Music. You can also download your content so that you can listen to or watch it when you're not connected to the Internet.
Before you can download content to listen to offline, you need to add it to your Library. Then, in the Music app on your iPhone, iPad, or iPod touch; in iTunes on your Mac or PC; or in the Apple Music app on your Android phone, find the item that you want to download, and follow these steps:
- On your iPhone, iPad, iPod touch, or Android phone: Tap Download .
- On your Mac or PC: Click Download .
You'll see when the download is complete.
If you have Automatic Downloads turned on, content automatically downloads to your device or computer when you add it to your Library. You won't see or .
Use the Watch app on your iPhone to add music to your Apple Watch.
You can download content on up to 10 devices. This content is accessible only when your Apple Music subscription is active.
The first time that you download content to your device, you might see a message that asks if you want to download it automatically.
- Tap Download Automatically to download all content automatically to your device. The next time you add an item to your Library, it also automatically downloads to your device.
- Tap Not Now to download the item later.
If you want to turn on Automatic Downloads for all content that you add to your Library in the future, go to Settings > Music, then scroll to the Downloads section and tap Automatic Downloads.