We report on the measurement and analysis of photoionisation, mass-analysed-threshold-ionisation and pulsed-field-ionisation zero-kinetic-energy photoelectron spectra of HD in the vicinity of the dissociative-ionisation thresholds H + + D(1s) + e − and H(1s) + D + + e − . The spectra were recorded via the v = 11-13 vibrational levels of the H and B outer wells of the H H 1 Σ + g and B B 1 Σ + u states and provide information on the weakly bound levels of the X + 2 Σ + g ground state of HD + with vibrational quantum numbers v + = 16-21 and rotational angular-momentum quantum numbers N + = 0-10. The spectra also reveal for the first time shape and Feshbach resonances of HD + located energetically above the H + + D(1s) dissociation limit. The structure and dissociation dynamics of the H and B states of HD and of the X + 2 Σ + g and A + 2 Σ + u states of HD + near the dissociation thresholds are strongly influenced by the g/u-symmetry breaking caused by the nuclear-mass asymmetry. KEYWORDS PFI-ZEKE photoelectron spectroscopy, shape and Feshbach resonances, g/u-symmetry breaking g and B B 1 Σ + u states and of HD + near the dissociation threshold, and (ii) the effects of the g/usymmetry breaking in the electronic states of HD and HD + . The earlier theoretical work of L. Wolniewicz and his coworkers on these topics [1-3] were extremely useful in guiding our analysis,