are static routes necessary with eigrp? 500 points

If 192.168.1.1 is sending you a default route, then you don't need the static route. If it isn't then you should ideally set it up a default route on the remote router and redistribute it into eigrp.

>I am running eigrp on the network is it still necessary to add a static route?
The whole idea of running any dynamic routing protocol is to do away with statics, except in your case the one default route. If you advertise this default route through eigrp to all the other routers, they will not need any statics at all.

However, I don't see where you are advertising your local 192.168.1.x subnet to the rest of the network.

To redistribute your local lan and a default :
Given:
ip route 0.0.0.0 0.0.0.0 192.168.1.1
  router eigrp 10
    redistribute static  <== send default
    redistribute connected   <== advertise local 192.168.1.0 subnet

Sorry, although ip route 0.0.0.0 0.0.0.0 192.168.1.1 is the current default, I want to drop this route because it points to the adsl line. I now want all traffic to  go down the leased line where the other side is 192.168.4.1. I still want to use the original default route as a backup. I suppose ican do this by adding a wait to it?

OK, the router that is a .4.1 will have a default and redistribute it.
Your end can add a higher admin cost the current default.
I think you meant "weight" where you said "wait" ?

no ip route 0.0.0.0 0.0.0.0 192.168.1.1
ip route 0.0.0.0 0.0.0.0 192.168.1.1 120  <== 120 is higher cost than EIGRP's 90
                                                                   so it will only use this route if the other one goes away

The default route that points to  
0.0.0.0 0.0.0.0 192.168.1.1

This points to an adsl line that I no longer wish to use!
I am no longer bothered about the the 192.168.1 network, as the adsl was only in place until we got the leased line working!

I now want ALL my traffic to go via the SERIAL 0/0/0:0
and only want to include the lan network
10.4.0.0 255.255.0.0      and the serial interface
192.168.40  0.0.0.3
The eigrp is set as
router eigrp 10
 network 10.4.0.0 0.0.255.255
 network 192.168.4.0 0.0.0.3
 network 192.168.4.0
 no auto-summary

If I "NO" the current default route, will my eigrp settings do the rest, or is a new default route still needed?

Also if i still wanted to use the adsl as a backup could I as you said put the old default route back on but change the admin distance to 120.

Does the fact that a default route has been added make the eigrp useless, as this default route will always be preferred over the eigrp?

Also for future reference. Does using default routes make eigrp invalid and
vice versa?
Isn't it right to say that by using eigrp it is not necessary to use default and static routes?

Thanks chaps I really appreciate the help

I like the idea of having a static default route, with a weight greater than any learned route.

You could have the ADSL also, with an even greater weight, as a backup.