The subject of the thesis is the design and implementation of an operating system kernel for the Cambridge Capability Computer (CAP). The kernel of an operating syst em is its most primitive level of facilities and forms the foundation stone a round which t he rest of the system is structured. The particular emphasis of the CAP kernel is concerned with protection - the control of access to information. The kernel uses the notion of capabilities to provide a flexible and controlled mechanism for the sharing of information within a computer system. The protection mechanisms include provision for the efficient control of access to memory as well as facilities for handling abstract resources like files and virtual peripherals. The kernel allows the introduction of new types of resources in addition to the basic set of hardware resourcee to permit user extension of the system. Attention is given to the problem of recall of privilege or revocation in capability systems and the kernel includes operations for both permanent and temporary revocation of particular access rights to information in a selective manner. In the past many of these functions have only been found in kernels implemented in user-level software which arc frequently cumbersome and inefficient. An examination is made of why this should be and·how efficiency and simplicity can be gained by a microprogrammed implementation. The thesis draws on the experience of a number of soft.ware kernels to discover the various design decisions that have to be made and the techniques that may be used to implement a successful kernel. The feasibility of the design arrived at by considering these issues is demonstratec1 by describinq its implementation on the Cambridge Capability Computer in terms of the primitives provided and the internal organisation of the proposed kernel. In an evaluation, the kernel is examined in the light of the analysis of other kernels to point out its strength s and weaknesses and to gain insights into the utility of the deign as a practical operating system kernel.