Biological evolution in a sequence space with random fitnesses is studied within Eigen's quasispecies model. A strong selection limit is employed, in which the population resides at a single sequence at all times. Evolutionary trajectories start at a randomly chosen sequence and proceed to the global fitness maximum through a small number of intermittent jumps. The distribution of the total evolution time displays a universal power law tail with exponent -2. Simulations show that the evolutionary dynamics is very well represented by a simplified shell model, in which the subpopulations at local fitness maxima grow independently. The shell model allows for highly efficient simulations, and provides a simple geometric picture of the evolutionary trajectories.Biological evolution often displays a punctuated dynamical pattern, in the sense that quiescent periods of stasis alternate with bursts of rapid change. A variety of mechanisms for punctuation have been proposed, which operate on different levels of the tree of life. On the largest scales of macroevolution, coevolutionary avalanches may play a role, which have been associated with self-organized criticality [1]. On the level of populations, punctuation due to rare, beneficial mutations has been observed in evolution experiments with bacteria [2]. Similar behavior has been found in simulations of RNA evolution, where stasis corresponds to diffusion on a neutral network, and a punctuation event marks the transition to another network of higher fitness [3].Possibly the simplest interpretation of punctuated evolution is in terms of a homogeneous population, represented by a localized distribution in some phenotypic or genotypic space, which evolves in a static, multipeaked fitness landscape [4]. Under conditions of strong selection and small mutation rate, such a population will rapidly climb a local fitness maximum, where it then resides for a long time, until a rare, large fluctuation allows it to cross the valley to a more favorable peak. At least in the limit of infinite population size [5], the mathematics of this process is closely related to physical problems such as noise-driven barrier crossing, tunneling [6] and variablerange hopping [7], and it is easy to show that the residence time at one peak can be vastly larger than the time required for the transition to the next [8]. In a rugged fitness landscape, the sequence of transitions forms an evolutionary trajectory, which probes the distribution of fitness peaks and the geometry of the landscape.In this Letter we investigate the statistics of such evolutionary trajectories in the framework of Eigen's quasispecies model [9,10]. We consider a population of individuals, each characterized by a binary genomic sequence σ of length N , which reproduce asexually and mutate in discrete time t. The total number of sequences is S = 2 N . An individual with genotype σ leaves A(σ) offspring in the next generation, and point mutations occur with probability µ per site and generation. In a mean field approximation, wh...