The bilayer structure of YBa2Cu3O6+x supports spin excitations that are either even or odd under a symmetry operation that exchanges two directly adjacent CuO2 layers. Both types of excitation have been observed in underdoped YBa2Cu3O6+x by inelastic neutron scattering. Even and odd response functions are split in energy. The temperature evolution in the normal state is parallel in both channels, but different behavior is observed in the superconducting state where a resonant enhancement is observed only in the odd channel. The measurements shed new light on the nature of interlayer interactions in the cuprates. (C) 1998 Elsevier Science Ltd. All rights reserved.