The following summary is based on Howell (2012):
At sea, occurs singly or in small groups. Howell (2012) describes the flight of Markham's Storm-Petrel as "generally fairly low, direct to slightly weaving, with buoyant wingbeats and glides, the wings held slightly arched. In calm to moderate winds, transiting flight unhurried with short bursts of fairly shallow, flicking wingbeats, interspersed with low wavelength glides on slightly arched wings. Foraging birds can switch to floppy, loose, and fairly deep wingbeats interspersed with short glides and abrupt swoops up over food. In calm conditions, also flies with steady flapping up to 3 meters abvoe the sea surface. In moderate to strong winds, weaves across the wind buoyantly with birds of loose, fairly deep, and quick flaps interspresed with banking and often prolonged, low-wavelength glides.... with wind astern, sometimes flies with more prolonged bouts of fairly quick flaps and short glides, at other times alternates a few quick flaps with long shearing glides. Forages into the wind with steady wingbeats, occasional pauses, and short glides, swooping up to drop on food and patter briefly, the wings raised in a V and bowed slightly at the wrist. Also picks at food while on the water, with wings raised and fluttered."
Behavior on the breeding grounds undescribed.