Not exactly sure what a "737-E" is, but...
normally, DME updating requires the best fix geometry of the (available) stations (within a specified distance from the aircraft). You're not going to get a very good fix if the station is too close or too far away... or if the angle formed between the first DME, the aircraft and the second DME is too acute or too obtuse. I believe the best angle is 90 degrees.
Depending on the type of DME Interrogator fitted to your aircraft, a single DME Interrogator can tune/scan/track many stations by itself....and I believe that if an interrogator fails (on a two DME Interrogator aircraft), you can still get a DME-DME update.
Were you looking for a more technical description than this?
Rgds.
Q
[ 18 September 2001: Message edited by: QAVION ]