This thesis is discussing the problem of stability of autonomous vehicle strings. First, the basic definitions and notations of vehicle strings are presented, in order to help the reader in understanding the rest of the document. Then a car following technology LPF-ASP (Leader and Predecessor Following with Adaptive Spacing Policy) is introduced, which shows promising performance. The starting point of this thesis is the transfer functions of a platoon that consists of LPF-ASP type vehicles. A platoon’s important performance property is the spacing error which is closely related to the stability of the platoon. An upper bound on the spacing error can be computed from the upper bound of the acceleration of the members of the string. There are existing solutions on how to compute the upper bound of the acceleration but they are very inaccurate in low frequencies. The aim of this thesis is to develop methods that give more accurate bound for the acceleration on low frequencies, too. To achieve that goal, I investigate several possible approaches, for example set theory and Lyapunov functions. The result is three different methods. At the end of the thesis, these methods and an already existing analytic method are compared.