I'm I into a vicious circle ? Newbie question .

[Daniel Pope]

Hello,
I have a dedicated server and I'm trying for the first time to setup a domain main. With your help (people from this list ) I did a good job locally.
Now I'm having problems with the remote. I registered with
Network Solutions the new name and I got an e-mail error message back telling me that I provided for name servers bad information.
My question is: I provided the first and second name  server my local name servers:
ns1.new_domain_name.com    MYIP ADRRESS and respectively
ns2.new_domain_name.com    MYIP ADRRESS.
Since the above 2 name servers are on my computer maybe nobody is able to resolve this (the curious is that I had to provide the IP   ) 
address names and in theis case I'm into a vicious ?!? 

If Network Solution  cannot resolve my local name servers  I'm I into a vicious circle ? In this case what kind of name server can I use ?  (I would strongly prever to use local ones if possible !!)

Or maybe can be a problem with the second server seetings (they share  the same IP address) !  

Any help would be greatly appreciated !