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A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A_p the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z Z_p such that Q/Z Z_p× Z_p. Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F_p in the variety of loops whose elements have order dividing p^2 and whose associators have order dividing p, wearXiv:1509.05727v1 fatcat:2zm7veljnrahxaw6z5ar7p7sme