Soyuz TM-3 was the fourth manned spacecraft to visit the Soviet space station Mir. It was launched in July 1987, during the long duration expedition Mir EO-2, and acted as a lifeboat for the second segment of that expedition. There were three people aboard the spacecraft at launch, including the two man crew of the week-long mission Mir EP-1, consisting of Soviet cosmonaut Aleksandr Viktorenko and Syrian Muhammed Faris. Faris was the first Syrian to travel to space, and as of November 2010, the only one. The third cosmonaut launched was Aleksandr Aleksandrov, who would replace one of the long duration crew members Aleksandr Laveykin of Mir EO-2. Laveykin had been diagnosed by ground-based doctors to have minor heart problems, so he returned to Earth with the EP-1 crew in Soyux TM-2.

Soyuz TM-3 landed near the end of December 1987, landing both members of the EO-2 crew, as well as potential Buran (spacecraft) shuttle pilot Anatoli Levchenko, who had been launched to Mir a week earlier aboard Soyuz TM-4.

Aleksandr Aleksandrov became Aleksandr Laveykin's replacement aboard Mir, becoming Yuri Romanenko's new partner. The visiting expedition observed Syria (Euphrat experiment) and conducted materials processing experiments, but also biological experiments.

Among other tasks, they carried out a series of measurements on the Bosra experiment, designed to obtain new information on the physical processes at work in the upper layers of the atmosphere and in the ionosphere, while yet another installation, the Ruckey, was used to purify genetically-engineered interferon and a drug to combat influenza. The purpose of yet another installation on Mir, Svetlana, was to isolate active microorganisms producing antibodies for use in stock farming.

The results of the Euphrates experiment were keenly awaited in Syria. While flying over that country, the cosmonauts carried out a series of visual observations, photographed its territory and performed a spectrometric survey. The data they collected would make it possible, with more accuracy, to define Syria's agro-resources, and help both geologists and hydrologists.

One of the experiments requiring special and unique care involved the use of the Kristallizator furnace. Even during designated rest periods, it had been determined that any movements by the cosmonauts could create sufficient vibrations to affect the delicate crystallization process. In the case of Mir, experimental work would not be carried out in the space station itself, but in one of the specially equipped experimental modules docked with it.

Syrian guest cosmonaut Muhammed Faris and Soviet cosmonaut Aleksandr Viktorenko returned to Earth in Soyuz TM-2 with Aleksandr Laveykin, who was diagnosed by ground-based doctors as having minor heart problems.