This thesis is concerned with the detection of very high energy 7-rays from isolated pulsars and objects that are not known to emit pulsed radiation, using the atmospheric Cerenkov technique. The first chapter summarises the processes by which celestial 7-rays can be generated and absorbed. A discussion of the criteria for selecting objects for study is given. The second chapter describes the atmospheric Cerenkov technique and gives a brief outline of its historical development. Details of the design and operation of the current Durham university V.H.E. 7- ray telescopes are given. The third chapter describes the standard analysis techniques used to search for pulsed and unpulsed emission. The fourth chapter presents results of new observations of four isolated pulsars. Upper limits to the V.H.E. 7-ray flux are derived for each pulsar. A summary of the results is given and conclusions drawn regarding the consequences of the observations for the most popular pulsar model. The fifth chapter deals with new analysis techniques that have been developed to test data for the presence of a signal which is not necessarily periodic. A number of different approaches is described. The results of these techniques when applied to simulated data are presented and conclusions are drawn regarding the relative effectiveness of the tests. The sixth chapter applies the most successful test to data from three objects. Upper limits to the flux from Centaurus A and SN1987aare derived from our observations. Evidence for V.H.E. 7-ray emission from Scorpius X-1 is presented, together with evidence that this emission is modulated with the period of the binary orbit of this system. The final chapter summarises the preceding results and conclusions and indicates areas where current research may lead to substantial improvements in telescope design and analysis techniques.