They are on the walls of a chapel next to the Sistine, closed to the public and rarely seen.
This is the first one, the Conversion of St. Paul.
Conversion of St. Paul (or Saul) by Michelangelo, in the Cappella Paolina, Palazzi Pontifici, Vatican (a public domain photo shown here)
The story is from the New Testament, the Acts of the Apostles, IX, 3. St. Paul, then called Saul, riding with his soldiers on a mission to persecute the Christians in Damascus, is struck down by a heavenly apparition and converted to Christianity.
A few who have had a look give it high points:
“The Fall of St. Paul cannot be represented with greater power than this,” wrote the great Swiss art critic Woefflin in 1899. “This is no longer the classical style; but neither is it senile indifference; Michelangelo outdoes himself in the energy of his representation…powerful and imperious lines slash through the painting like lightning; grave and concentrated masses alternate with broad empty areas.”
But most critics were disappointed:
“Nothing in these two compositions is reminiscent of the great Michelangelo: confusion in the whole, barrenness in the details, poverty of color…” G. Clausse, Les San Gallo, Paris 1902
“The flexibility, the elasticity, the sharpness with which Michelangelo had always treated the nude have all disappeared…” J. A. Symonds, 1893
“The defects, hidden in the Last Judgment by the overpowering qualities, fill both the Pauline frescoes.” P. Toesca, Michelangelo in the Encyclopedia Italiana, XXIII, Rome, 1934
Michelangelo was old.
Vasari says, as if to excuse him: “These scenes, which he painted at the age of seventy-five, were the last pictures he did; and they cost him a great deal of effort, because painting, especially in fresco, is no work for men who have passed a certain age.”
Here is the other fresco, Michelangelo’s very last painting, the Crucifixion of St. Peter. The story is not in the New Testament but was an old tradition. St. Peter was crucified upside down.
Crucifixion of St. Peter, by Michelangelo (a public domain photo shwon here)
“…the languid left-overs of his strength.” The Gentleman’s and Connoisseur’s Dictionary of Painters, London, 1770
“The lack of the study of nature is even more evident than in the Judgment…” C. H. Wilson, 1876
“You esthetes are missing the point of these works,” said some of the critics. “They present us with a Michelangelo renewed in his old age, in possession of a spiritual certainty…so grand and firm.” (V. Mariani, 1946). The frescoes are about the religious experience. They show the “two essential moments of the religious life or human asceticism: conversion and martyrdom”. (Argan, 1963)
These critics go so far as to affirm that the Conversion of St. Paul reflects Michelangelo’s own conversion. The fallen St. Paul is the artist himself: it is a self-portrait.
See this photo enlarged here.
These have been meticulously restored in a process that began in 2004. See this.