These two psalms constitute the third reading of the Psalter at Matins on Great Feasts and certain Sundays (in some places, on all Sundays), and on all other Vigil or Polyeleos-rank feasts. The name "polyeleos" arises from the repetition of the phrase "for His mercy endureth forever" in Psalm 135. On the three Sundays which immediately precede Great Lent, Psalm 136 (LXX) "By the waters of Babylon..." is added to the other two Psalms.
In parish practice, the Psalms are usually abbreviated. This is one of the most festive moments of a Vigil, when the Royal Doors are opened, and the clergy come out of the altar and cense the entire church. 
- The Festal Menaion (Tr. Mother Mary and Archimandrite Kallistos Ware, Faber and Faber, London, 1984), p. 556ff.
- Fr. Victor Potapov, Polyeleios The All-night Vigil Service—The Evening Sacrifice, September 25, 2007.