  Pseudoprocesses, constructed by means of the solutions of higher-order
heat-type equations have been developed by several authors and many related
functionals have been analyzed by means of the Feynman-Kac functional or by
means of the Spitzer identity. We here examine even-order pseudoprocesses
wrapped up on circles and derive their explicit signed density measures. We
observe that circular even-order pseudoprocesses differ substantially from
pseudoprocesses on the line because - for $t> \bar{t} > 0$, where $\bar{t}$ is
a suitable $n$-dependent time value - they become real random variables. By
composing the circular pseudoprocesses with positively-skewed stable processes
we arrive at genuine circular processes whose distribution, in the form of
Poisson kernels, is obtained. The distribution of circular even-order
pseudoprocesses is similar to the Von Mises (or Fisher) circular normal and
therefore to the wrapped up law of Brownian motion. Time-fractional and
space-fractional equations related to processes and pseudoprocesses on the unit
radius circumference are introduced and analyzed.
