Guiding light at the nanoscale is usually accomplished using surface plasmons. However, plasmons propagating at the surface of a metal sustain propagation losses. A different type of surface excitation is the Dyakonov surface wave. These waves, which exist in lossless media, were predicted more than two decades ago but observed only recently. Dyakonov surface waves exist when at least one of the two media forming the surface exhibits a suitable anisotropy of refractive indexes. Although propagating only within a narrow range of directions, these waves can be used to create modes supported by ultrathin films that confine light efficiently within film thicknesses well below the cutoff thickness required in standard waveguides. Here, we show that 10 nm and 20 nm dielectric nanosheets of aluminium oxide clad between an anisotropic crystal (lithium triborate) and different liquids support Dyakonov-like modes. The direction of light propagation can be controlled by modulating the refractive index of the cladding. The possibility of guiding light in nanometre-thick films with no losses and high directionality makes Dyakonov wave modes attractive for planar photonic devices in schemes similar to those currently employing long-range plasmons.