In which type of wave do particles move both perpendicular and parallel to the wave direction?

Particles in a surface wave move in a circular motion, which means they exhibit both perpendicular and parallel movement relative to the direction in which the wave is traveling. In a surface wave, such as those observed on the surface of water, the particles at the surface move up and down as well as back and forth, creating a combination of transverse and longitudinal wave characteristics. This dual movement allows energy to be transferred across the surface, which is why surface waves are distinct from purely transverse or longitudinal waves.

In contrast, longitudinal waves have particles that oscillate parallel to the direction of wave propagation, while transverse waves have particles that move perpendicular to the wave's direction. Mechanical waves are a broader category that includes both transverse and longitudinal waves but do not define the specific movement pattern described in the question.