In this PhD thesis. I mainly discuss two topics: Strange Stars （SSs） and Gamma-Ray Bursts （GRBs）.The concept of neutron star is proposed as early as in the 1930s, and pulsars were discovered and identified as neutron stars in the late sixties. To many people this identification is quite convincing, and it is always regarded as a good example of a successful identification in modern astrophysics. However, we should be aware that pulsars may not, be neutron stars at all, they muy be Strange Stars. This possibility stems from the hypothesis proposed by Witten and Farhi & Jaffe in 1984: the absolute ground state of hadrons might bo strange quark matter （i.e., the energy state of strange stars may be lower than that of neutron stars for rather wide range of QCD paramelers）. This conjecture is of obvious importance to modern physics, and has attracted a lot, of attentions. In 1991, a successful international workshop on strange quark matter was held in Denmark. Today, scientists all over the world are still Irving hard to resolve this problem through laboratory experiments and/or astrophysical tests.Gamma-ray bursts （GRBs） have puzzled astronomers since their accidental discoveryin the late sixties. The BATSE detector onboard the Compton-GRO satellite has been detecting one burst per day for the last six years. Its findings have revolutionized our ideas about the nature of these objects. They have shown that GRBs are at cosmological distances. This idea was accepted with difficulties at first. The recent discovery of X-ray, optical and radio afterglows from some GRBs due to the Italian/Dutch satellite BeppoSAX has strongly confirmed the cosmologieal origin. Cosmologieal GRBs release 1050 1054crgs in a few seconds, making them the most （electromagnetically） luminous objects in the Universe. The simplest, most conventional, and practically inevitable, interpretation of these observations is that GRBs result from the conversion of the kinetic energy of ultra-relativistic particles or possibly the electromagnetic energy of a Poynting flux to radiation in an optically thin region. This generic "fireball" model has also been confirmed by the afterglow observations. The "inner engine" of GRB is well hidden from direct observations, but we still could infer some hints.Currently SSs and GRBs arc very active areas in high energy astrophysics. Under the direction of Professor Lu Tan, together with other collaborators in our group. I have done some researches in these fields and published several papers in astrophysical journals. They include: two papers in A&A;one in ApJ;one in MXRAS;three in Chinese Physics Letters;and two in other Chinese journals. Some of these results have been cited by other researchers. I present some of our lindings in this thesis, of which the structure and the contents are sketched as follows:Chapter 1 is a brief review on strange stars. The history, the physical background. the dynamics of strange quark matter, the so called strange dwarfs, the difference between strange stars and neutron stars, and many other related astrophysics are brielly introduced.Chapter 2 discusses I.he normal matter crusts of SSs. This chapter is mainly basedon oik1 of our rcbcareheb: we have developed a self-consistent model to depict the electric, field at the snrfa.ro of a SS, wn find that t.lir maximum curst density is only about one lil’lh of the usually assumed neutron drip density. Detailed results have b<:t,’ii published in A&A （19D7） mid Chinebe Phybics Letters （1997）. These results ha\e already boon cited by Jos Madden.Chapter 3 is a. brief introduction to CRBs. Emphasis is put on the recent progresses, i.e.. GRR afterglow observations and the rosmologioal firoball model.Chapter 4 discusses the post-burst evolution of adiabatic GRB remumitb. We liavo evaluated the process numerically, anil find that the remnant will cease to be highly rolativistic several days after the main GRB. So we need lo imosligate the marginally relativistie phase. The results have been published in MNR.AS （1998）.Chapter 5 discusses afterglows from Soft Gamma Repeal,crs. We suggest thai, we could test the fireball model by monitoring X-ray and optical i-ifteriilowb from Soft Gamma Repeaters. Detailed results were published in Cliinrsr Physics Letters （1998） and Journal of Nanjing University （1998）.Chapter fi studies tlie evolution of a.diaba.tir GRR remnants. Emphasis has been put on the transition from the highh relativisiie phase to the iion-rclativistic phase. which, according to our calculation, should happen much earlier than previously exported. The results have been published in A&A （Lett.） （1998）. Our results were cited by Meszaros. Roes and Wijors.Chapter 7 studies afterglows from ’’realistic" GRB remnants. The remnant evolves from highly radiative stage to a.diaba.tir. stage. We dovelopo a dynamical model to describe this process. The results have been accepted for publication in ApJ.Chapter S developos a "generic" dynamir.al model for GRR remnants, i.e.. the model is applicable to bol.h radiative and adiabatie blast,waves, in both relativistie and non-relativibtic phases. The results have been i-iccepted for publication in Chinese Physics Letters and/or submitted to Y1NRAS.Chapter 9 is a brief summary of the whole thesib. I personally believe tin-it the most confusing enigma of GRRs, the "inner engine", might bo closely related to SSs.In short, in this thesis, in addition lo the necessary reviews on SSs （chapter 1） and GRBb （Chapter 3）. I mainly present my own researches in these fields. My interests are concentrated in two aspects: （i） 1 study I,he maximum density of SS crusts and lind that previous models did not satisfy the mechanical balance condition. After considering this condition, the maximum density should only be about one fifth of the neutron drip density （4.3 x 10u g riu"1’） （Chapter 2）: （ii） 1 sl.udy the general ease of the dynamical evolution of GRB remumitb. which may be either highly radiative or adiabatic, ultra-relative tic or non-relalivistic （Chapter 4 8）. 1 compare my results with observations and lind that the fireball model agrees with observation:? quite well.