Track-density scaling has become the main enabler for the continuing increase in areal density and cartridge capacity in tape storage systems. However, as the track density in tape systems is scaled from around 10 ktpi today to 100 ktpi, new challenges are posed to track-following servomechanisms, which will have to provide a positioning accuracy of the order of a few nanometers. In this paper, advanced control techniques are presented that address these challenges. A novel method based on the signals obtained from dual servo channels is proposed for the suppression of high-frequency disturbances, which originate from compressional waves that oscillate between the tape-path rollers and are excited by the tape-head friction. Furthermore, the tape-velocity dependent system delay is experimentally characterized and subsequently used to optimize the track-following control design. Results obtained with a high-SNR magnetic tape based on perpendicularly-oriented barium ferrite (BaFe) particles, a prototype head actuator, and an experimental tape transport system are presented. A position error signal with a standard deviation of less than 6 nm over a wide range of operating tape velocities is demonstrated.