Hello Elmar,

Thank you for reporting the bug. Please attach a sample document, as this makes it easier for us to verify the bug. 
I have set the bug's status to 'NEEDINFO'. Please change it back to 'UNCONFIRMED' once the requested document is provided.
(Please note that the attachment will be public, remove any sensitive information before attaching it. 
See https://wiki.documentfoundation.org/QA/FAQ#How_can_I_eliminate_confidential_data_from_a_sample_document.3F for help on how to do so.)

(In reply to Xisco Faulí from comment #1)
> Hello Elmar,
> 
> Thank you for reporting the bug. Please attach a sample document, as this
> makes it easier for us to verify the bug. 
> I have set the bug's status to 'NEEDINFO'. Please change it back to
> 'UNCONFIRMED' once the requested document is provided.
> (Please note that the attachment will be public, remove any sensitive
> information before attaching it. 
> See
> https://wiki.documentfoundation.org/QA/
> FAQ#How_can_I_eliminate_confidential_data_from_a_sample_document.3F for help
> on how to do so.)

Thank you for the speedy response, Xisco Fauli
I was testing v5.3 in a LM MATE VM. the version is 
Version: 5.3.0.0.beta2+
Build ID: 6eb2598a5d052220c6b569d1b49e80800850ac06
CPU Threads: 1; OS Version: Linux 4.4; UI Render: default; VCL: gtk2; Layout Engine: new; 
TinderBox: Linux-rpm_deb-x86_64@70-TDF, Branch:libreoffice-5-3, Time: 2016-12-14_22:50:48
Locale: en-ZA (en_ZA.UTF-8); Calc: group

I have tested the same document there without a problem.

I will now reinstall the the version I downloaded from main website (http://www.libreoffice.org/download/libreoffice-fresh/) - the prerelease version at the bottom of the page.

I did a "normal" install of v5.3 from the downloaded files. synaptic  reflects v5.3, yet when I open writer or calc, it reflects the version number as Version: 5.2.5.0.0+ (which I reinstalled after purging LO.)

I will now remove LO and do the reinstall of 5.3 again.

yesterday, when I attempted to change format of some text to italics, the way the screen flashed it seemed as if it was looping in some way. 

Today, it does not do this, but gets the same error on saving.

I created a new document, but got the same "styles.xml" problem - and I cannot save the document, as before.

So I cannot send you an example.

I removed LO again, and downloaded fro DEV (http://dev-builds.libreoffice.org/daily/libreoffice-5-3/Linux-rpm_deb-x86_64@70-TDF/current/)

Installed again - same problem, cannot save.

I thought it might have been because there was something missing, so I removed LO again, installed LO 5.1.4 from Software Manager, then installed 5.3 again.
5.1.4 works fine, 5.3 still has save problem.

Removed LO again and reinstalled the last working version I was using: 5.2.5, downloaded from DEV site.

works fine.

When I tried 5.3 the first time, this was from the DEV site. 5.2.5 was active. 5.3 did not work, but I thought this was because of a conflict with 5.2.5 so I did not investigate it further.

Please note that in the VM, LO 5.1.4 and 5.3 are working quite happily together. But the OS is LM MATE 18

Seems to be an issue with LMC 18.1? Is there some dependence on MONO? This has been worked out of LMC18.1. This is the only thing I can think of.