::Per Hinsley, 
 :::They [Allied cryptanalysts] were hardly ever rivalled by Axis success in reading our ciphers. There were two major exceptions to the lack of success by the Axis against Allied ciphers. One was that they did have some success in reading a British naval cipher which was for a longish time also shared with the American navy in relation to convoy escorting.They were successful in reading that for a long period from 1940 to the end of '42. And the other was that they didn't exactly capture but they managed to extract of copy of the cipher that was being used by the American Military Attache in Cairo for a period when Rommel was at his most dangerous. And from that too the Germans obtained some great advantage.But generally speaking, except possibly in relation to the convoy cipher, there was never any great cryptanalytical rivalry. The Germans were completely outclassed in terms of Ultra. The Italians also made very little progress against any important allied cipher. 
 ::German cryptanalysis of British naval ciphers is also discussed a bit in Stephen Budiansky, "Battle of Wits" chapter 8, "Paranoia is our profession".  The Germans also broke the US M-209 machine cipher but that was only used for lower level traffic AFAIK.  There is some info in the M-209 article.