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Spatiotemporal focusing, or simultaneous spatial and temporal focusing (SSTF) of ultrashort pulses, has drawn more and more attention because of its various applications in microscopy, photoactivation for biological studies, and high precision three-dimensional (3D) material processing. This conception of focusing relies on the fact that the axial intensity is highly localized because the pulse duration is not its shortest until all the spectral components are fully overlapped. In this paper, we present the spectral chirps and intensities evolution in SSTF at the focus based on generalized Fresnel diffraction theory. By directly solving the Fresnel diffraction integration equation, the spectral chirps up to 4th-order are obtained analytically. After that, the intensities evolution at the focus is carried out by numerical simulations as well as mathematical investigations. Especially, the appearance of pulse front tilt (PFT) and intensity plane tilt (IPT) in SSTF are discussed in detail with the help of the given spectral chirps. Keywords: Ultrashort pulses, Simultaneous spatial and temporal focusing, Chirps, Pulse front tilt, Intensity plane tilt