To provide comprehensive (i.e. rapid and sensitive) MS-MS analysis, the inventor employs a time-nested separation, using two time-of-flight (TOF) mass spectrometers. Parent ions are separated in a slow and long TOF1, operating at low ion energy (1 to 100 eV), and fragment ions are mass analyzed in a fast and short TOF2, operating at much higher keV energy. Low energy fragmentation cell between TOF1 and TOF2 is tailored to accelerate fragmentation and dampening steps, mostly by shortening the cell and employing higher gas pressure. Since separation in TOF1 takes milliseconds and mass analysis in TOF2—microseconds, the invention provides comprehensive MS-MS analysis of multiple precursor ions per single ion pulse. Slow separation in TOF1 becomes possible with an introduction of novel TOF1 analyzers. The TOF-TOF could be implemented using a static TOF1, here described on the examples of spiratron, planar and cylindrical multi-pass separators with griddles spatial focusing ion mirrors. Higher performance is expected with the use of novel hybrid TOF1 analyzers, combining radio frequency (RF) and quadratic DC fields. RF field retains low-energy ions within TOF1 analyzer, while quadratic DC field improves resolution by compensate for large relative energy spread.