  The classical Eulerian polynomials $A_n(t)$ are known to be gamma positive.
Define the positive Eulerian polynomial $\mathsf{AExc^{+}}_n(t)$ as the
polynomial obtained when we sum excedances over the alternating group. We show
that $\mathsf{AExc^{+}}_n(t)$ is gamma positive iff $n \geq 5$ and $n \equiv 1$
(mod 2). When $n \geq 4$, and $n \equiv 0$ (mod 2) we show that
$\mathsf{AExc^{+}}_n(t)$ can be written as a sum of two gamma positive
polynomials.
  Similar results are shown when we consider the positive type-D and type-D
Eulerian polynomials.
  Finally, we show gamma positivity results when we sum excedances over
derangements with positive and negative sign. Our main resuls is that the
polynomial obtained by summing excedance over a conjugacy class indexed by
$\lambda$ is gamma positive.
