Neutron stars are believed to be formed by supernova explosions of massive stars. However, in spite that a number of radio pulsars have been discovered (>500 objects: Taylor, Manchester, & Lyne 1993), the number of pulsar/supernova remnant association is very limited. Also, in spite that the expected number of young pulsars with ages less than $\thicksim$ 2000 yr is $\thicksim$ 40 or so in, the Galaxy for a reasonable estimate on the supernova rate, only a few pulsar are known to have characteristic ages less than 2000 yr. In this study, I have observationally examined the X-ray emission characteristics of young neutron stars not by studying the known (radio) pulsars, but by studying the Crab-like supernova remnants (plerions) and (nonthermal) composite type supernova remnants. Totally 6 objects, G11.2--0.3, G27.4+0.0 (Kes 73), G119.5+10.2 (CTA 1), Gl30.7+3.l (3C58), G292.0+1.8, and G332.4-0.4 (RCW 103), are analyzed, of which two objects are candidates for historical remnants of supernovae, SN 386 (G11.2-0.3) and SN 1181 (Gl30.7+3.l). In this sample, no object has a known associated radio pulsar. For RCW 103, a 69 ms pulsation has been reported based on the $Ginga$ LAC observation (Aoki et al. 1992). For Kes 73, 12 s pulsation from the central source, lE 1841-045 has been reported by $ASCA$ and $ROSAT$ observations (Aoki 1995: Vasisht & Gotthelf 1997). The current study involves (if possible, spatially resolved) spectroscopy and searches for coherent pulsations, the latter is the prime signature of the existence of a neutron star powering the non-thermal Crab-like nebula. All the X-ray emissions have been found to be reasonably explained in terms of a combination of several components, the thin thermal emission from the SNR shell, non-thermal emission from the synchrotron nebula, pulsed emission from the neutron star, and the soft blackbody type radiation from the neutron star surface. However, as has been suggested in the previous works in different contexts, it is found that the objects are extremely heterogeneous, suggesting the variety of nature of young neutron stars. The large effective area, hard X-ray imaging capability of $ASCA$ makes the signal to noise ratio in pulsar searches higher than previous instruments in several ways. At above $\thicksim$ 2 keV, the photoelectric absorption of emissions from objects on the Galactic plane is negligibly small, and the moderate spatial resolution is compensated for by the appropriate filtering by the pulse height (energy), thereby obtaining a large signal to noise ratio for an embedded, hard compact source within the diffuse soft emission at low Galactic latitude. Thus, with the $ASCA$, pulsations have successfully been detected from a 65 ms pulsar within the SNR G11.2-0.3, from a 69 ms pulsar in the vicinity of the SNR RCW 103, and from a 12 s pulsar within the SNR Kes 73. In the following chapters, I first summarize the overview of the current knowledge on supernovae, supernova remnants, and pulsars, with emphasis upon the latest observational results. Then the instruments onboard the $ASCA$ observatory are explained before going into detailed analysis of each object. After showing results on each object in the ascending order in Galactic longitude, I will discuss the evolutionary sequence of this class of objects. Then the characteristics of the synchrotron nebulae are discussed in terms of the MHD model of the nebulae. Finally, I summarize the current study and the future prospects are presented. In the appendix, basic physics of pulsars and supernova remnants are summarized.