The formation of laser-induced periodic surface structures (LIPSS) on two different dielectrics of K9 glass and fused silica upon irradiation in ambient conditions and in vacuum with multiple femtosecond (fs) laser pulse sequences at different pulse durations (35 fs, 260 fs, and 500 fs) was studied experimentally. Three types of LIPSS, so-called high-spatial-frequency LIPSS (HSFL), low-spatial-frequency LIPSS (LSFL), and supra-wavelength periodic surface structures (SWPSS) with different spatial periods and orientations were identified. The appearance was characterized with respect to the experimental parameters of laser fluence and number of laser pulses per spot. The crater morphologies - including nanoripples, periodic microgrooves, quasiperiodic microspikes, and central smooth zone - were observed by scanning electron microscope (SEM). The supra-wavelength structures exhibit periodicities, which are markedly, even multiple times, higher than the laser excitation wavelength. The SWPSS were formed with a broader range of laser fluences, upon the longer laser pulse durations (260 fs and 500 fs) and/or on the lower band-gap dielectrics (K9 glass), due to the deeper effective light penetration depths and thicker viscous surface layers formation. The HSFL were observed on the higher band-gap dielectrics (fused silica) and within a certain narrow laser parameter window. The formation mechanisms of LIPSS were also discussed.