If you have an older computer/laptop with less than 128MB RAM and a slow CPU, you might be better off using the cli-installer.

In tests, mainly by drg (thanks), you should be able to install all versions of antiX using the cli-installer with as little as 64MB RAM. Installing base and core should also be ok with as low as 48MB RAM. YMMV. (Don't expect miracles though after install on boxes less than 128MB RAM)

It is best to have your partitions already set up before booting the live medium. A swap partition is recommended. You should note how the partitions are labelled ie as sda1 or hda1 as you will need this information during install.
If you are not sure, before running the script, login as root and type blkid or fdisk -l (You could also use fdisk to set up the partitions before running the installer script)

1. Boot live-medium.
At grub/menu Press F1 for information and cheatcodes available, F2 to set the language you want, F3 to set the Timezone.
If your locale is not shown in F2, simply type the language like this: lang=ca_ES for Catalan.
If the timezone is not shown in F3, simply type like this: tz=Europe/Madrid
Press Enter when ready.

2. Login as root, password root. If your locale uses a non US keyboard, you may need to toggle Alt Shift to type correctly. Then type cli-installer

3. You will be asked if you want to repartition the disk. Default reply is No. If you choose to repartion the disk, then cli-installer will start cfdisk. If you need help with cfdisk, see here (thanks to TinyCore):
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You will be asked to choose type of file system for the partition from ext2, ext3 or ext4.

4. Once the partitions have been set up, you will then be asked where the root partition will be. Make sure you type the correct partition label eg sda1 or hda1 or sda2 etc.
cli-installer tells you it is deleting the contents of chosen partition.

5. You are asked if you want to use separate /home yes/no? Default is No. If you chose yes, you will be prompted to type in the partition address eg sda3.
You will then be asked to choose type of file system for the partition from ext2, ext3 or ext4.

cli-installer will inform you that antiX-M11 will be installed to chosen partition and when finished it will say 'File copy done'.

6. You will be asked where to place the grub bootloader, Install grub on MBR? Y/n. Default is Yes. No will install to your root partition.

7. You will be asked for a Computer name? Accept default or type in your own.

8. You will be asked to set up your user account. You are asked to type a
User name
then Password
and Password again

9. You will be asked to set up your root(admin) account by typing
Password for root
and the Password again

10. Once finished you should get a message that installation was ok and prompted to reboot.

11. Type Reboot.