The Mudros Armistice (which ended hostilities between the Allies and the Ottomans) partitioned much of the Ottoman Empire into occupation zones, but the Empire still retained its monarchic government. Sultan Mehmed VI was, however, intended to be more of a figurehead for the occupying forces (at least temporarily) than a leader in his own right. Mehmed cooperated with the Allies rather willingly, and this rubbed some members of the Ottoman Army the wrong way. After all, the Ottomans had fought hard and well -- with a much cleaner military record at the end of the war than the other Central Powers -- and they were now being asked to repudiate everything for which they had fought.

One major source of tension was the arrival of Greek soldiers as Allied occupiers. Unlike the British, French, and Italians, the Greeks were historical rivals of the Ottomans, and saw their role as occupiers as the first step in restoring Greece to its rightful (Byzantine) borders. While the Allied entrance into Istanbul was relatively peaceful and uncontested, the Greek landing in Smyrna featured fighting, looting, and sectarian violence; to make matters worse, it seemed like the Greeks would try to annex Smyrna, while the Allies were content to simply administer their portions of the country.

With the country thus in danger, resistance began to be organized on a political and military scale -- but Mehmed, essentially held captive in Constantinople, did nothing to endorse it. When Mehmed signed the Treaty of Sèvres in 1920, he gave legitimacy to the Allied dismantling of the old empire and angered the Turks, who undertook their War of Independence without him. The Turks vented their frustration by declaring the new country a republic; they would repudiate Mehmed just as Mehmed had repudiated his empire.

Mehmed fled Constantinople soon after the Turkish Republic formally abolished the Ottoman Empire and the sultanate. His brother Abdülmecid was named caliph in his stead (less than two years later, the caliphate, too, was abolished) -- but not sultan. The Ottoman Empire was finally dead in theory as well as in practice.

Sources: Midnight at the Pera Palace: The Birth of Modern Istanbul, Charles Starr King

The Decline & Fall of the Ottoman Empire, Alan Palmer

Well as far as the Hapsburg Empire is concerned, it sort of just...fell apart. Prior to the war the population of the Hapsburg Empire had consisted of no fewer than ten different ethnicities and languages. It consisted of German Austrians, Hungarians, Slovenes, Croats, Czechs, Slovaks, Poles, Serbs, Romanians, Italians, and Ruthenians (Ukrainians). Now this level of ethnic diversity had resulted in the Hapsburg Empire being rife with ethnic tensions, further enflamed by the waves of nationalism that were prevalent all throughout Europe in the 19th century. After 4 years of destructive war the nationalistic sentiment among the nationalities of the empire had come to full boil. Food shortages, terrible human losses, and inspired by the bolshevik revolution that had taken place in Russian in 1917, widespread strikes began to take place all throughout the Hapsburg Empire, demanding bread and an end to the war, and culminating in active opposition to the government. Not only strikes among workers but mutinies in the armed forces further strained the weakening empire. On October 16 1918, in an attempt to hold together his crumbling empire, the Emperor Charles issued a proclamation federalizing the Empire along ethnic lines, which really only served as the basis for the empires liquidation. On October 7 the Poles had proclaimed a union of all Polish people with the capital in Warsaw, declaring their independence, on October 28 the Czechs formed an independent republic, and the Southern Slavs were advocating for union with Serbia. This all occurred technically before the end of the war, so the Hapsburg armies continued to fight for a country that in essence no longer existed. Finally it all ended when the Emperor Charles issued a statement in November waiving all rights of political authority, effectively marking the end of the Hapsburg Empire.

I hope this helped answer your question, but if you have any more please ask.

Sources: For God And Kaiser: The Imperial Austrian Army 1619-1918 by Richard Basset.

        A History of the Hapsburg Empire by Robert A Kahn

Hey, this recent post I made may be helpful for you:

• What about World War 1 brought about the fall of empires globally?

However the other two replies to this thread have covered the topic wonderfully, so look there first!