Materials processing utilizing ultrashort near-infrared (NIR) laser pulses with duration in the range of tens to hundreds of femtoseconds (1 fs = 10(-15) s) has attracted a great deal of interest in the scientific and industrial world recently. Unfortunately, a number of materials that often exhibit great technological and scientific importance are transparent in NIR, making it very difficult to process them by laser radiation in this spectral range. Here, we present a new method for the efficient structuring of the surface of materials by applying femtosecond NIR laser pulses simultaneously with a weak extreme ultraviolet (XUV) beam, which leads to very strong radiation-matter interaction, bringing a dramatic increase in the surface processing speed. A laser system providing 5 mJ, 820 nm, 32 fs, 10 Hz pulses was used to generate high-order harmonics with the strongest spectral line at 21 nm and with a conversion efficiency of similar to 5%. The two beams were focused on the samples by using an off-axis paraboloidal multilayer mirror. As an example, we present the results of the surface nanostructuring of thin films of amorphous carbon and poly(methyl methacrylate) deposited on bulk substrates. We discuss the physical mechanisms that lead to the laser-induced periodic surface structures when our method is used.