Author Institution: Department of Chemistry, Department of Astronomy & Astrophysics,; and the Enrico Fermi Institute, University of Chicago, Chicago, IL 60637Recent observations of highly deuterated molecules such as ND3β and D2βCO in prestellar cores and their explanation as due to the extraordinarily high deuterium fractionation of H3+β to H2βD+, HD2+β and D3+β,} \textbf{591}, L41 (2003).} have revealed the importance of observing other deuterated variants of fundamental molecular ions that also play pivotal roles in interstellar chemistry. We have launched an infrared project to study such ions systematically in order to provide their approximate rotational constants for millimeter wave spectroscopists. \vspace{2ex} We are presenting our work on the near-infrared spectroscopy of CHD+ and CD2+β. While our search for interstellar CH2+β based on our infrared} \textbf{153}, 738 (1992).} and near-infrared} \textbf{121}, 11527 (2004).} laboratory spectra has not been successful due to its extremely high reactivity, its detection in the future is expected in diffuse clouds since it is the intermediate between the abundant CH+ and yet to be observed but very important CH3+β. CH2+β and its deuterated species are also of special interest for theoretical study because of their unique intramolecular dynamics, i.e., the Renner-Teller interaction and quasi-linearity. \vspace{2ex} Using He-dominated liquid-N2β cooled plasmas (βΌ10 Torr) containing a small amount (βΌ0.1 Torr) of CH4β, CH2βD2β, CD4β and their mixtures, we are searching for the spectra of CD2+β and CHD+ in the near-infrared from 10,500 cmβ1 to 12,500 cmβ1 with our Ti:sapphire laser spectrometer that combines velocity modulation and phase modulation with heterodyne detection for near shot-noise-limited sensitivity. Our search is based on the \textit{ab initio} calculation by Bunker, Jensen and colleagues} \textbf{225}, 33 (1997).} which predicts the A~(0,5,0)1 and A~(0,4,0)1βX~(0,0,0)0 bands of CD2+β, and the A~(0,4,0)1βX~(0,0,0)0 band of CHD+ as the most intense in the region