can pop3 & imap run on the same server

hi
im installing 2 kind of web base email UebiMiau and squirrelmail. Uebimaiu uses pop3 and squirrelmail use imap but i only have one mailserver. My question is can this two pop3 and imap run on the same server at the same time? If YES will the2 (pop&imap) receive the same email messeges if someone send me an email…

Thanks