In this paper, we analyze a new asynchronous rumor spreading protocol to deliver a rumor to all the nodes of a largescale distributed network. This protocol relies on successive pull operations involving k different nodes, with k = 2 or k = 3, and called k-pull operations. Specifically during a k-pull operation, an uninformed node a contacts k − 1 other nodes at random in the network, and if at least one of them knows the rumor, then node a learns it. We perform a detailed study in continuous-time of Θ k,n , the total time needed for all the n nodes to learn the rumor. We obtain, for k ∈ {2, 3}, the mean value, the variance and the distribution of Θ k,n together with their asymptotic behavior when the number of nodes n tends to infinity.