ABSTRACT Self-gravitating gaseous filaments exist on many astrophysical scales, from sub-pc filaments in the interstellar medium to Mpc scale streams feeding galaxies from the cosmic web. These filaments are often subject to Kelvin–Helmholtz Instability (KHI) due to shearing against a confining background medium. We study the non-linear evolution of KHI in pressure-confined self-gravitating gas streams initially in hydrostatic equilibrium, using analytic models and hydrodynamic simulations, not including radiative cooling. We derive a critical line mass, or mass per unit length, as a function of the stream Mach number and density contrast with respect to the background, μcr(Mb, δc) ≤ 1, where μ = 1 is normalized to the maximal line mass for which initial hydrostatic equilibrium is possible. For μ < μcr, KHI dominates the stream evolution. A turbulent shear layer expands into the background and leads to stream deceleration at a similar rate to the non-gravitating case. However, with gravity, penetration of the shear layer into the stream is halted at roughly half the initial stream radius by stabilizing buoyancy forces, significantly delaying total stream disruption. Streams with μcr < μ ≤ 1 fragment and form round, long-lived clumps by gravitational instability (GI), with typical separations roughly eight times the stream radius, similar to the case without KHI. When KHI is still somewhat effective, these clumps are below the spherical Jeans mass and are partially confined by external pressure, but they approach the Jeans mass as μ → 1 and GI dominates. We discuss potential applications of our results to streams feeding galaxies at high redshift, filaments in the ISM, and streams resulting from tidal disruption of stars near the centres of massive galaxies.