Well, I admit, I stumbled across that: I created a virtual machine in my local network and wanted to use it in Microsoft Azure. Well, of course - although I've read it a thousand times - the source machine was a VHDX file...
So the VHDX file needs to be converted to VHD format. Happily, I found the solution quickly :
Converting Hyper-V .vhdx to .vhd file formats for use in Windows Azure
Open PowerShell on a Hyper-V Host and run the Convert-VHD command which is available since Windows Server 2012 - see here.
Convert-VHD -Path C:\VM\MyVM.vhdx -DestinationPath c:\VM\MyNewVM.vhd
That's it! Thx Courtenay Bernier for the tip!