We present a MUSE and KMOS dynamical study 405 star-forming galaxies at redshift z = 0.28–1.65 (median redshift z¯= 0.84). Our sample is representative of the star-forming “main-sequence”, with star-formation rates of SFR = 0.1–30M⊙ yr−1 and stellar masses M⋆ = 108–1011 M⊙. For 49 ± 4% of our sample, the dynamics suggest rotational support, 24 ± 3% are unresolved systems and 5 ± 2% appear to be early-stage major mergers with components on 8–30 kpc scales. The remaining 22 ± 5% appear to be dynamically complex, irregular (or face-on systems). For galaxies whose dynamics suggest rotational support, we derive inclination corrected rotational velocities and show these systems lie on a similar scaling between stellar mass and specific angular momentum as local spirals with j⋆ = J /M⋆ ∝ M 2/3 ⋆ but with a redshift evolution that scales as j⋆ ∝ M 2/3 ⋆ (1 + z) −1 . We also identify a correlation between specific angular momentum and disk stability such that galaxies with the highest specific angular momentum (log(j⋆ / M2/3 ⋆ ) > 2.5) are the most stable, with Toomre Q = 1.10 ± 0.18, compared to Q = 0.53± 0.22 for galaxies with log(j⋆ / M2/3 ⋆ )