Install the avahi packages:

sudo apt-get install avahi-daemon avahi-dnsconfd avahi-discover avahi-utils

Install libnss-mdns:

sudo apt-get install libnss-mdns

Check that /etc/nsswitch.conf has the following line:

hosts:    files mdns4_minimal dns [NOTFOUND=return] mdns4

Verify hosts

service avahi-daemon status
getent hosts 

ping debian.local.
avahi-resolve -n debian.local.

Files

• /etc/avahi/avahi-daemon.conf
• /etc/nsswitch.conf

Referencias