Modern space communication systems often need high-power low-frequency (UHF, L-, S-, and C-band) low-pass filters (LPFs) with wide stopbands extending to Ka-band and beyond. Current design approaches frequently fail to meet these requirements completely. This paper proposes a new coaxial LPF concept and design methodology. The LPF consists of an array of cavity elements, which operate with transverse electromagnetic mode (TEM) and transverse magnetic (TM)-coupled resonances, and thus achieve a frequency response with a reflection zero at DC and transmission zeroes at targeted stopband locations. The design method is based on positioning the cavities in a quasi-periodic order, which efficiently spreads the transmission zeroes over the stopband, while keeping the characteristic impedance matched to the input/output interfaces over the passband. This design concept yields an ultra-wide, continuous and modal spurious-free stopband, while maintaining a low insertion loss, high peak power capacity, and low sensitivity to production tolerances.