  Let $X=G/K$ be a Riemannian symmetric space of the noncompact type and
restricted root system $BC_2$ or $C_2$ (except $G=SO_0(p,2)$ with $p>2$ odd).
The analysis of the meromorphic continuation of the resolvent of the Laplacian
of $X$ is reduced from the analysis of the same problem for a direct product of
two isomorphic rank-one Riemannian symmetric spaces of the noncompact type
which are not isomorphic to real hyperbolic spaces. We prove that the resolvent
of the Laplacian of $X$ can be lifted to a meromorphic function on a Riemann
surface which is a branched covering of the complex plane. Its poles, that is
the resonances of the Laplacian, are explicitly located on this Riemann
surface. The residue operators at the resonances have finite rank. Their images
are finite direct sums of finite-dimensional irreducible spherical
representations of $G$.
