My bad!!! You miss the priority of the MX record
Here is your new db.xx.xx.xx.xx

mail:~# named-checkzone -d 113/29.xx.xx.xxx.in-addr.arpa. /etc/bind/db.118.xx.xx.xxx
loading "113/29.xx.xx.xxx.in-addr.arpa." from "/etc/bind/db.118.xx.xx.xxx" class "IN"
/etc/bind/db.118.xx.xx.xxx:10: 113/29.xx.xx.xxx.in-addr.arpa: bad owner name (check-names)
zone 113/29.xx.xx.xxx.in-addr.arpa/IN: loaded serial 11


mail:~# nslookup mail.mydomain.com
Server: 127.0.0.1
Address: 127.0.0.1#53

Name: mail.mydomain.com
Address: xxx.xx.xx.118

mail:~# nslookup xxx.xx.xx.118
Server: 10.0.0.1
Address: 10.0.0.1#53

** server can't find 118.xx.xx.xxx.in-addr.arpa: NXDOMAIN

Sorry is bothering you, but I must conclude that to turn my mail server...

Thanks.

Did you remove the "check-names ignore;" from named.conf?
The fact is that your bind version does not like the "/" in the zone name, but should not complain using the option above. I don't have this problem using 9.6.0-P1 with my reverse zone 0/28.x.x.x and in fact I don't recall this behavior the last 3ys using different bind versions.
Contact again your ISP and ask him if you can use just 113.xx.xx.xx.in-addr.arpa for the zone name. If you can, then do the necessary changes in named.conf and in db.xx.xx.xx and try again.
Or you can upgrade your bind version and see if it works.
Another thing to note is that the response for the reverse lookup is from 10.0.0.1 and not from localhost, assuming you ran the 2 nslookups from the same box. Use dig, so you can control the name server to use:

I didn't remove the "check-names" in the named.conf file is still there:

zone "113/29.xx.xx.xxx.in-addr.arpa"{
notify no;
type master;
check-names ignore;
file "/etc/bind/db.118.xx.xx.xxx";


I did the tests requested:



mail:~# dig @mail.mydomain.com 11-xxx.xx.xx.118.in-addr.arpa ns

; <<>> DiG 9.3.4-P1.1 <<>> @mail.mydomain.com 11-xxx.xx.xx.118.in-addr.arpa ns
; (1 server found)
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 11817
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;11-xxx.xx.xx.118.in-addr.arpa. IN NS

;; AUTHORITY SECTION:
xx.xx.xxx.in-addr.arpa. 9350 IN SOA ns4.telemar.net.br. root.ns4.telemar.net.br. 2008062401 21600 3600 1209600 432000

;; Query time: 0 msec
;; SERVER: xxx.xx.xx.118#53(xxx.xx.xx.118)
;; WHEN: Tue Apr 7 11:06:13 2009
;; MSG SIZE rcvd: 106


===========================================================================

mail:~# dig mail.mydomain.com @127.0.0.1

; <<>> DiG 9.3.4-P1.1 <<>> mail.mydomain.com @127.0.0.1
; (1 server found)
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 19129
;; flags: qr aa rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;mail.mydomain.com. IN A

;; ANSWER SECTION:
mail.mydomain.com. 86400 IN A xxx.xx.xx.118

;; AUTHORITY SECTION:
mydomain.com. 86400 IN NS mail.mydomain.com.

;; Query time: 0 msec
;; SERVER: 127.0.0.1#53(127.0.0.1)
;; WHEN: Tue Apr 7 11:06:20 2009
;; MSG SIZE rcvd: 69


======================================================================

mail:~# dig -x xxx.xx.xx.118 @127.0.0.1

; <<>> DiG 9.3.4-P1.1 <<>> -x xxx.xx.xx.118 @127.0.0.1
; (1 server found)
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 51534
;; flags: qr rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 3, ADDITIONAL: 3

;; QUESTION SECTION:
;xxx.xx.xx.118.in-addr.arpa. IN PTR

;; ANSWER SECTION:
xxx.xx.xx.118.in-addr.arpa. 3522 IN PTR i118-xx-xx-xxx.s10.a044.ap.plala.or.jp.

;; AUTHORITY SECTION:
18.17.118.in-addr.arpa. 3522 IN NS ns-tk062.ocn.ad.jp.
18.17.118.in-addr.arpa. 3522 IN NS dns-cz1.plala.or.jp.
18.17.118.in-addr.arpa. 3522 IN NS dns-cz2.plala.or.jp.

;; ADDITIONAL SECTION:
dns-cz1.plala.or.jp. 86321 IN A 210.153.1.164
dns-cz2.plala.or.jp. 86321 IN A 60.43.59.164
ns-tk062.ocn.ad.jp. 86321 IN A 202.234.232.206

;; Query time: 0 msec
;; SERVER: 127.0.0.1#53(127.0.0.1)
;; WHEN: Tue Apr 7 11:06:26 2009
;; MSG SIZE rcvd: 218

I think I should call TELEMAR company that is responsible for my network link. And they ask for the delegation of my DNS server so that it will resolve the name. What do you think that????

You should already have call them. I was continuously told you to do so, as they have to delegate you the subnet xx.xx.xx.113/29. From the dig outputit's obvious that you don't have authority on this zone

I knew I had to call them, but I thought to talk with them, the server should first resolve the name internally.
And he is not doing it.

mail:~# dig xxx.xx.xx.118

; <<>> DiG 9.3.4-P1.1 <<>> xxx.xx.xx.118
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 28569
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;xxx.xx.xx.118. IN A

;; AUTHORITY SECTION:
. 10800 IN SOA A.ROOT-SERVERS.NET. NSTLD.VERISIGN-GRS.COM. 2009040701 1800 900 604800 86400

;; Query time: 84 msec
;; SERVER: 127.0.0.1#53(127.0.0.1)
;; WHEN: Tue Apr 7 18:02:29 2009
;; MSG SIZE rcvd: 106


SEE IT HERE: status: NXDOMAIN

If you want to use dig to do reverse lookups you need the "-x" option:
The fact that it's not resolving the ip, is because the xx.xx.xx.xx/24 authority (that is telemar.net.br) has not give you the authority over the xx.xx.xx.113/29 subnet.

I go call for TELEMAR today to resolve that. So now I have a doubt, I was examining the files and appeared the following questions:

I need put the @ before the statements:

such as:

@ IN NS mail.mydmain.com.
@ IN MX 10 mail.mydmain.com.
www IN A xxx.xx.xx.114
118 IN PTR mail.mydmain.com.


Thanks.

@ is the same as the ORIGIN and it's not necessary (specially if you have the ORIGIN defined). Only in the SOA record is needed.
So speak with your ISP, so they give you the delegation of your subnet chuck and if you have further questions I'll be glad to help.
Meanwhile consider upgrading bind, so it does not complain for the "/" in the in-addr.arpa zone name.

Regards

So please me a hint on how atulizar the BIND, because if I give the command apt-get install bind9 it will install the same I already have.

Thanks...

I'm not familiar with debian and its flavours, but after a little search I found this. If this is not suit your debian version search the same site for other packages.

These packages you showed me is for Debian lenny and I'm using Debian etch. I believe it will not serve...

As I told you I'm not familiar with these debian versions. You can ask here at the LQ debian forum how to get the latest bind.
And you can always compile bind from source.

I'll see if I find something in the forum, but anyway thanks for helping me, and I hope to continue counting on your help.

Thanks....