The first is Allegri's Miserere, a setting of Psalm 50/51 which mixes polyphony and plainchant. The text of that psalm is penitential and begins accordingly:
"Have mercy on me, O God, according to thy great mercy. And according to the multitude of thy tender mercies blot out my iniquity. Wash me yet more from my iniquity, and cleanse me from my sin. 5For I know my iniquity, and my sin is always before me...."
The second is the Kyrie from Palestrina's Missa Papae Marcelli.