  We compute the one-loop effective action and the conformal anomaly associated
with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal
L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact
type. The explicit form of the zeta functions and the conformal anomaly of the
stress-energy momentum tensor is derived.
