A cowl structure comprises first and second cowl members that are independent components. A first cowl member is attachable, by a latch mechanism, to a support structure of the outboard motor. The second cowl member is attachable by a latch mechanism, to both the first cowl member and the support structure. The first cowl member extends across a rear portion of the outboard motor and at least partially along both port and starboard sides of the outboard motor. The second cowl member extends across a front portion of the outboard motor and at least partially along the port and starboard sides of the outboard motor. In a preferred embodiment, the second cowl member also extends partially over a top portion of the outboard motor and over a rear portion of the outboard motor.