As a result of the industrial deployment of real-time systems, there is an increasing demand for methods to perform safe and tight calculation of the worst case execution time (WCET) of programs. The WCET is a necessary prerequisite for guaranteeing correct timing behaviour of real-time systems. WCET calculation means to find the path, often among a huge number of paths, that takes the longest time to execute. The calculation is based on path information for the program, such as the maximum number of iterations in loops and identification of paths that are never executed. In most existing WCET analysis methods, this information is given as manual annotations by the programmer. In this thesis we present a method which automatically calculates path information for object-oriented real-time programs by static analysis. Thus, the method can be used in automating the WCET analysis, thereby relieving the programmer from the tedious and error-prone manual annotation work. The method, which is based on abstract interpretation, generates safe but not necessarily exact path information. A trade-off between quality and calculation cost has to be made, since finding the exact information is a complex, often intractable problem for non-trivial programs. We show how the general abstract interpretation theory can be used, in a structured way, to approximate the semantics of an imperative or object-oriented programming language. We have chosen to analyze RealTimeTalk (RTT), an object-oriented language based on Smalltalk, and have developed a prototype tool which implements our analysis for a subset of the language. We show that the tool is capable of analyzing programs with a complexity which would make manual annotation of the program all but trivial.