What does the message unable to set gid=ddd or uid=ddd (euid=ddd): local delivery to ... transport=ttt mean?

Have you remembered to make Exim setuid root? It needs root privilege if it is to do any local deliveries, because it does them as the user . Note also that the partition from which Exim is running (where the binary is installed) must not have the nosuid mount option set. You can check this by looking at its /etc/fstab entry (or /etc/vfstab, depending on your OS).

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