  We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of
freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin
and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The
models are exactly solvable by Kitaev's parton approach, and we obtain
long-wavelength descriptions for both Majorana liquids. The MOL has one gapless
mode and power law correlations in energy at incommensuare wavevectors, while
the SU(2) MSL has three gapless modes and power law correlations in spin,
spin-nematic, and local energy observables. We study the stability of such
states to perturbations away from the exactly solvable points. We find that
both MOL and MSL can be stable against allowed short-range parton interactions.
We also argue that both states persist upon allowing $Z_2$ gauge field
fluctuations, in that the number of gapless modes is retained, although with an
expanded set of contributions to observables compared to the free parton mean
field.
