  In this paper, we uncover the elusive level crossings in a subspace of the
asymmetric two-photon quantum Rabi model (tpQRM) when the bias parameter of
qubit is an even multiple of the renormalized cavity frequency. Due to the
absence of any explicit symmetry in the subspace, this double degeneracy
implies the existence of the hidden symmetry. The non-degenerate exceptional
points are also given completely. It is found that the number of the doubly
degenerate crossing points in the asymmetric tpQRM is comparable to that in
asymmetric one-photon QRM in terms of the same order of the constrained
conditions. The bias parameter required for occurrence of level crossings in
the asymmetric tpQRM is characteristically different from that at a multiple of
the cavity frequency in the asymmetric one-photon QRM, suggesting the different
hidden symmetries in the two asymmetric QRMs.
