Here I identify novel stability features in flapping flight. Implications may shift the current scientific consensus that flying animals, particularly insects, must actively monitor and respond to even slight perturbations to maintain control in pitch and roll, and allow engineers to recreate these capabilities in flying robots. Results are consistent with co-directional inertial and viscous effects working together to damp rotations. This could explain flight stability across a broad range of body sizes, speeds, and flapping frequencies. I propose a previously undescribed, likely ubiquitous class of passive “inertio-viscous” damping. Flapping wings move, so rotational perturbations on the time scale of halfstrokes manifest as wing position/orientation changes later in the flapping cycle. My novel results show these (at least partially) passive (inertia-based) kinematic responses push on the air to produce torques that oppose the initial perturbation. I then identify key design elements which future flapping-wing micro air vehicles could employ to exploit these stability effects. This emerges from a series of three experiments exploring roll and pitch dynamics in hawkmoth Manduca sexta. In the first, I coaxed moths to follow a light and described their lateral maneuver mechanics. I concluded roll is heavily damped, and positive coupling between roll and lateral acceleration, negative coupling between roll and lateral velocity, and countertorque from wing motion around the roll axis, are relevant (viscous/velocity) damping factors. In the second, I launched miniature cannonballs at moths and described their pitch recovery mechanics. I concluded inertial (and viscous) resistance of wing stroke plane to the pitch impulse (and rotational velocity) helps create pendular stability in mid-air. Gyroscopic (and viscous) reactions to pitch impulses (and rotational velocity) manifest as deviations to wing kinematics that further damp pitch, indicating reinforcing roles for inertia and drag in flapping flight stability. In the third, I glued T-bars on moths to create weight imbalances during hover. Results reinforce my conclusions about damping and roll/pitch-associated wing kinematics, show flexibility helps compensate for off-axis loads, and associate a novel wing kinematic with roll torque that suggests gyroscopic and pendular damping mechanisms also complement viscous/velocity-based damping in roll.