本文以 Henstock-Kurzweil 积分（简称 HK 积分）为理论工具研究了一类一阶拟线性偏微分方程 Cauchy问题解的存在唯一性. 根据该类问题与常微分方程组 Cauchy 问题的关系，可将此问题的求解归结为验证相应的常微分方程组 Cauchy 问题存在唯一连续可微解的条件. 本文首先归纳总结常微分方程、常微分方程组 Cauchy 问题在 HK 积分意义下解的存在唯一性理论以及常微分方程组 Cauchy 问题 HK 解关于参数的连续依赖性理论，在此基础上放宽了一类一阶常微分方程组 Cauchy 问题解的存在性条件，并给出了一阶拟线性偏微分方程 Cauchy 问题解的存在性唯一性证明，并辅以例子说明本文给出的判别性条件在应用中的实际作用. 该理论是微分方程解的经典理论的一个补充，将一类一阶拟线性偏微分方程在 Lebesgue 积分空间上的解推广到HK 积分空间.

The existence and uniqueness of solutions to the Cauchy problem for a first-order quasi-linear partial differential equation is studied in the setting of Henstock-Kurzweil integral(“HK integral”for short) in this paper. According to the relationship between this problem and the Cauchy problem for ordinary differential equations, the approach can be concluded to verifying the conditions under which the uniqueness, continuity and differentiability of solutions to Cauchy problems for ordinary differential equations are satisfied. The theories of the existence, uniqueness and the dependence on parameters of the Henstock-Kurzweil-solutions to the Cauchy problem for ordinary differential equations are summarized first, to be the basis of applying simplified conditions to a certain type of Cauchy problem for ordinary differential equations and giving the proof of the existence and uniqueness of solutions to the Cauchy problem for a first-order quasi-linear partial differential equation, which is in order to strengthen the specific usage of the conditions presented in this page. These theories can be regarded as an extension of the classical results and a generalization of the solutions to the Cauchy problem for a first-order quasi-linear partial differential equation in the Lebesgue setting to the Henstock setting.