The Dorman part numbers you list are the fittings that screw into the 
cooler built into the radiator.  Unless those are leaking you shouldn't 
need to.  Usually they leak where the rubber quick disconnects are 
crimped to the metal line.
Most people just buy the transmission cooler lines with the normal metal 
flares on the end and get normal hose nipples for cooler and use bulk 
transmission cooler hose and hose clamps, it's simpler than the "quick 
disconnects" and if it leaks you just replace the hose and hose clamps 
rather than the entire hard line.  (Like 
http://www.dormanproducts.com/p-26695-624-393.aspx).
M.B.
On 3/17/2012 12:11 PM, Chris Reck wrote:
> Hi,
>
> I need to replace my transmission oil cooler lines.  Both are leaking at
> both ends.  Do I just need to get the two tubes (sending and return), or di
> I also need the Oil cooler line connectors (Dorman 800-713 and/or 800-751)?
>
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