Turning gear apparatus (10) for rotating a shaft (11) comprises a rotary drive arrangement (12) and a transmission system including a pivot arm (20). The rotary drive arrangement (12) is fixed, for example to a vessel hull (14), and the pivot arm (20) is pivotable between a first, shaft-disengaged, position and a second, shaft-engaged position where the rotary drive arrangement (12) is operably coupled to the shaft (11), thereby permitting control over rotation of the shaft (11) by the rotary drive arrangement (12).