Variational studies of the rovibrational spectra of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>DT</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/

In this work we study the last two hydrogen molecular ion isotopologues, ${\mathrm{DT}}^{+}$ and ${\mathrm{T}}_{2}^{+}$, for which high-precision calculations have not yet been made. We obtain the nonrelativistic solutions of the Schr"odinger equation for the wide range of vibrational states up to the highest possible vibrational $1s{\ensuremath{\sigma}}_{g}$ state which are of spectroscopic precision. Transition amplitudes for electric dipole transitions, leading-order relativistic corrections, and coefficients of the effective hyperfine structure Hamiltonians for both ${\mathrm{DT}}^{+}$ and ${\mathrm{T}}_{2}^{+}$ are also calculated.