  Let G be a rank two finite group, and let $\cH$ denote the family of rank one
p-subgroups of G, at all primes where G has p-rank two. We show that a rank two
finite group G which satisfies certain group-theoretic conditions admits a
finite G-CW-complex X with isotropy in $\cH$, whose fixed sets are homotopy
spheres. Our construction provides an infinite family of new non-linear
G-CW-complex examples.
