Handbook of ROCOR Liturgical Practice:

Precisely when do we say the threefold Prayer of the Third Hour?

The threefold Prayer of the Third Hour (‘O Lord, Who didst send down Thy most Holy Spirit at the third hour…’) is to be included in the Divine Liturgy exactly as it is appointed in the Service Book, without alteration. That is to say, after the prayer ‘Again we offer unto Thee this rational and bloodless service…’, the Priest says ‘O God cleanse me a sinner’ three times with bows, and then the threefold Prayer of the Third Hour with uplifted hands, with the responses by the Deacon.

A modern custom of moving the prayer ‘Again we offer unto Thee this rational and bloodless service…’ to a position after the threefold prayer is not the tradition of the ROCOR, and not blessed to be practiced in our Diocese.

Under no circumstances is the threefold Prayer of the Third Hour to be ommitted from the Divine Liturgy.