In the Spring of 329, Alexander crossed the large desert between the city Bactra (Balkh, near modern Mazâr-e Sharîf) and the river Oxus in pursuit of the Persian leader Bessus. The best description of the death march is that of the Roman author Quintus Curtius Rufus, who based his account on older Greek sources.
Section 7.5.1-16 of his History of Alexander the Great of Macedonia was translated by John Yardley.
Alexander in the Bactrian desert
[7.5.1] Entrusting Bactria to Artabazus, Alexander left his baggage and equipment there under guard while he entered the desert areas of Sogdia with a light-armed force, leading the troops by night.
[7.5.2] The lack of water, mentioned above, is such that desperation produces a parching thirst even before a natural craving to drink appears. For 75 kilometers no trace of water is to be found.
[7.5.3] The heat of the summer sun scorches the sands and, when these start to heat up, everything on them is baked as if by perpetual fire.
[7.5.4] Then a misty vapor thrown up by the burning heat of the earth obscures the daylight, giving the plains the appearance of one vast, deep ocean.
[7.5.5] Travel by night seemed bearable because dew and the early morning freshness would bring relief to their bodies; but with the dawn comes the heat, draining with its aridity all natural moisture and deeply burning the mouth and the stomach.
[7.5.6] So it was their resolution that failed first, and then their bodies. They were unwilling to stop and unwilling to go on.
[7.5.7] A few had followed the advice of people who knew the country and stored up some water. This slaked their thirst for a short time, but then the increasing heat rekindled their craving for water. Consequently, all the wine and oil in anyone's possession was consumed, too, and such was the pleasure they gained from drinking it that they had no fear of thirst in the future.
[7.5.8] Subsequently, the liquid they had greedily drained put such a weight on their stomachs that they could neither hold up their weapons nor continue their journey, and the men who had been without water now seemed to be more fortunate than they themselves, since they were forced to spew up the water they had immoderately consumed.
[7.5.9] These urgent problems distressed Alexander. His friends stood around him and begged him to remember that his intrepid spirit was all that could restore the fortunes of his languishing army.
[7.5.10] At this point he was met by two of the men who had gone ahead to select a camp-site. They were carrying skins of water to bring relief to their sons who, they knew, were suffering from severe thirst in Alexander's column.
[7.5.11] On meeting the king one of them opened a skin, filled a cup he was carrying, and offered it to him. Alexander took it. Then he asked for whom they were carrying the water and learned it was for their sons.
[7.5.12] He returned the cup, as full as when it was offered to him, saying: "I cannot bear to drink alone and it is not possible for me to share so little with everybody. Go quickly and give your sons what you have brought on their account."
[7.5.13] Finally, around early evening, Alexander reached the river Oxus, but most of the troops had been unable to keep pace with him. He had beacons lit on a mountain-peak so that men having difficulty keeping up could see they were not far from camp.
[7.5.14] Those at the front of the column, quickly revived by something to eat and drink, were ordered by Alexander to fill skins, or any vessels that could serve for carrying water, and to bring relief to their comrades.
[7.5.15] But some men gulped the water down too greedily and died from blockage of the windpipe - and the number of these exceeded the numbers Alexander had lost in any battle.
[7.5.16] As for the king, he stood at the point where the troops were arriving, still wearing his cuirass and without having taken any food or drink, and he did not leave to take refreshment until the entire column had passed him.