I'm not seeing this in my tests.

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Which template are you using?

In the Editor Global Configuration, what have you selected for the Editor Styles option?

the editor styles option is set to my own css.

This is where the Styles list gets the classes from. What is in this css file?

What happens if you set the Editor Styles option to "Template CSS Files"?

In Editor Profiles -> Editor Parameters -> Typography, is Editor Styles set to Inherit?

In Editor Profiles -> Plugin Parameters -> Style Select, do your parameters look like this?

I can't really do much more without seeing this for myself. You can see on the demo site that the Styles list is functional in JCE Pro 2.9.63 - https://demo.joomlacontenteditor.net

I will need a login to your site to investigate further - https://www.joomlacontenteditor.net/contact/site-login

Template is Purity III and the editor styles option is set to my own css.

Are you using an editor.css file for your own css? If you are, what does this editor.css file include? Can you post a link to your site front-end?

In your template's css folder, eg: templates/purity_iii/css create a file called editor.css and add the following to the file:

@import url('bootstrap.css');
@import url('template.css');

Thie will style the editor content correctly and populate the Styles list.

Tinymce does not have a Styles list that operates in the same way as JCE so the comparison is not applicable.

This is not a bug in JCE as it does not occur in other situations (see the demo site - https://demo.joomlacontenteditor.net) only on your site.

The only way to resolve this further is for me to have a look at your site. Please send me a login - https://www.joomlacontenteditor.net/contact/site-login