Question: Were Operation Nordwind and the Battle of Peleliu both fought in World War II?

Context paragraphs:
Operation Zahnarzt: Operation Zahnarzt (literally "Dentist") was a plan by the Germans to eliminate the Third Army during World War II.  The plan of Operation Zahnarzt was to immediately come after Operation Nordwind.  The plan was to initiate a pincer movement to encircle and destroy the 3rd US Army.

With the Old Breed: With the Old Breed: At Peleliu and Okinawa is a World War II memoir by Eugene Sledge, a United States Marine.  Since its first publication in 1981, "With the Old Breed" has been recognized as one of the best first-hand accounts of combat in the Pacific during World War II.  The memoir is based on notes Sledge kept tucked away in a pocket-sized Bible he carried with him during battles he fought at Peleliu and Okinawa.

Colmar Pocket: The Colmar Pocket (French: "Poche de Colmar" ; German: "Brückenkopf Elsaß" ) was the area held in central Alsace, France, by the German Nineteenth Army from November 1944 to February 1945, against the U.S. 6th Army Group during World War II.  It was formed when 6th AG liberated southern and northern Alsace and adjacent eastern Lorraine, but could not clear central Alsace.  During Operation Nordwind in December 1944, the 19th Army attacked north out of the Pocket in support of other German forces attacking south from the Saar into northern Alsace.  In late January and early February 1945, the French First Army (reinforced by the U.S. XXI Corps) cleared the Pocket of German forces.

Herbert J. Ray: Rear Admiral Herbert James Ray (1 February 1893 – 3 December 1970) was an officer in the United States Navy who served in World War I and World War II.  A 1914 graduate of the Naval Academy, he served on the submarines USS "H-2" and "N-3" during World War I.  In March 1942, as Chief of Staff and Aide to the Commandant of the Sixteenth Naval District, Rear Admiral Francis W. Rockwell, he participated in General Douglas MacArthur's escape from the Philippines.  In Australia, he served with MacArthur's General Headquarters, Southwest Pacific Area staff.  In September 1943, he became Captain of the battleship USS "Maryland" , which he commanded in the Battle of Tarawa, Battle of Kwajalein, Battle of Saipan and the Battle of Peleliu.  In October 1944, he participated in the Battle of Surigao Strait, in which "Maryland" joined the other battleships in engaging the Japanese battleships "Fusō" and "Yamashiro" and their escorts.  Ray left "Maryland" in December 1944, and was appointed Deputy Director of the Naval Division of the US Control Group Council for Germany.  After VE Day, he became the Junior United States Member of the Tripartite Naval Commission in Berlin.  He retired from the Navy on 30 June 1949, and received a tombstone promotion to rear admiral due to his combat decorations.

Operation Nordwind: Operation North Wind (German: "Unternehmen Nordwind" ) was the last major German offensive of World War II on the Western Front.  It began on 31 December 1944 in Alsace and Lorraine in northeastern France, and ended on 25 January.

Battle of Peleliu: The Battle of Peleliu, codenamed Operation Stalemate II by the United States military, was fought between the U.S. and the Empire of Japan during the Mariana & Palau Campaign of World War II, from September to November 1944, on the island of Peleliu.

Herrlisheim: Herrlisheim is a commune in the Bas-Rhin department in Grand Est in north-eastern France.  The town dates from the 8th century.  Herrlisheim was the scene of very heavy fighting during "Operation Nordwind", an offensive launched by the German Army during World War II that inflicted considerable damage to the town.

Peleliu: Peleliu (or Beliliou) is an island in the island nation of Palau.  Peleliu forms, along with two small islands to its northeast, one of the sixteen states of Palau.  The island is noted as the location of the Battle of Peleliu in World War II.

Order of battle for Operation Nordwind: This is the order of battle of German and Allied forces during Operation Nordwind in World War II

827th Tank Destroyer Battalion: The 827th Tank Destroyer Battalion was a tank destroyer battalion of the United States Army active during the Second World War.  It was activated in April 1942 as a segregated African American unit, deploying to Europe at the end of 1944 and attached to 12th Armored Division.  It saw action during Operation Nordwind in January 1945, where elements of the battalion performed creditably.  However, its overall combat record was marred by severe disciplinary problems and insufficient training.  It was withdrawn in February, and assigned to rear-area duties; while it nominally remained active for the remainder of the war, it had been effectively disbanded.

Supporting paragraphs: Operation Nordwind Battle of Peleliu
Answer: yes