A method of contactlessly advancing a continuous stream of substrates, comprising: - providing a process tunnel, extending in a longitudinal direction and bounded by at least a first and a second wall, said walls being mutually parallel and spaced apart so as to allow a substantially flat substrate, oriented parallel to the walls, to be accommodated there between; - providing a first gas bearing by providing a gas flow alongside the first wall, and providing a second gas bearing by providing a gas flow alongside the second wall; - providing a substantially flat substrate in between the first wall and the second wall, such that it is floatingly accommodated between the first and second gas bearings, said substrate comprising two main surfaces, a laterally extending trailing edge and a laterally extending leading edge; characterized by - providing the gas flow alongside the first wall in a substantially lateral direction; - providing the gas flow alongside the second wall in a substantially lateral direction; - bringing about a first longitudinal division of the process tunnel into a plurality of pressure segments, wherein the first and second gas bearings (124, 134) in a pressure segment have an average gas pressure that is different from an average gas pressure of the first and second gas bearings in an adjacent pressure segment such that for at least three consecutive pressure segments the average gas pressures are set such that, viewed in a longitudinal direction, the pressure is monotonically decreasing or increasing and a pressure differential (ΔP z) over a length of the substrate is substantially constant so as to induce a substantial constant substrate velocity over the at least three consecutive pressure segments. - providing a process tunnel, extending in a longitudinal direction and bounded by at least a first and a second wall, said walls being mutually parallel and spaced apart so as to allow a substantially flat substrate, oriented parallel to the walls, to be accommodated there between; - providing a first gas bearing by providing a gas flow alongside the first wall, and providing a second gas bearing by providing a gas flow alongside the second wall; - providing a substantially flat substrate in between the first wall and the second wall, such that it is floatingly accommodated between the first and second gas bearings, said substrate comprising two main surfaces, a laterally extending trailing edge and a laterally extending leading edge; - providing the gas flow alongside the first wall in a substantially lateral direction; - providing the gas flow alongside the second wall in a substantially lateral direction; - bringing about a first longitudinal division of the process tunnel into a plurality of pressure segments, wherein the first and second gas bearings (124, 134) in a pressure segment have an average gas pressure that is different from an average gas pressure of the first and second gas bearings in an adjacent pressure segment such that for at least three consecutive pressure segments the average gas pressures are set such that, viewed in a longitudinal direction, the pressure is monotonically decreasing or increasing and a pressure differential (ΔP z) over a length of the substrate is substantially constant so as to induce a substantial constant substrate velocity over the at least three consecutive pressure segments.