Quasirandom Rumor Spreading Abstract: In the classical randomized rumor spreading model, we start with one node of a graph knowing a ``rumor''. Then in each round each node that knows the rumor chooses a neighbor at random and informs it of the rumor. Results of Frieze and Grimmett 1985 show that in a complete graph on n vertices, this simple protocol succeeds in spreading the rumor from one node to all others within (log_2(n) + ln(n))(1 + o(1)) rounds. For the network being a hypercube or a random graph G(n,p) with p <= (1 + epsilon)(log n)/n, again O(log n) rounds suffice, see Feige, Peleg, Raghavan, and Upfal 1990. We propose and analyse a quasirandom analogue of the randomized rumor spreading problem described above. In the quasirandom model, we assume that each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold. In addition, we also show an O(log n) bound for sparsely connected random graphs G(n,p) with p=(log n + f(n))/n, where f(n) goes to infinity and f(n)=O(log log n). Here, the classical model needs Theta(log^2(n)) rounds.