  In this paper we give a meromorphic continuation of the spectral zeta
function for semiregular Non-Commutative Harmonic Oscillators (NCHO). By
``semiregular system'' we mean systems with terms with degree of homogeneity
scaling by $1$ in their asymptotic expansion. As an application of our results,
we first compute the meromorphic continuation of the Jaynes-Cummings (JC) model
spectral zeta function. Then we compute the spectral zeta function of the JC
generalization to a 3-level atom in a cavity. For both of them we show that it
has only one pole in 1.
