  We study conjugacy closed loops (CC-loops) and power-associative CC-loops
(PACC-loops). If $Q$ is a PACC-loop with nucleus $N$, then $Q/N$ is an abelian
group of exponent 12; if in addition $Q$ is finite, then $|Q|$ is divisible by
16 or by 27. There are eight nonassociative PACC-loops of order 16, three of
which are not extra loops. There are eight nonassociative PACC-loops of order
27, four of which have the automorphic inverse property.
  We also study some special elements in loops, such as Moufang elements, weak
inverse property (WIP) elements, and extra elements. In a CC-loop, the set of
WIP and the set of extra elements are normal subloops. For each $c$ in a
PACC-loop, $c^3$ is WIP, $c^6$ is extra, and $c^{12} \in N$.
