Abstract: It is well known that, as $n$ tends to infinity, the probability of satisfiability for a random 2-SAT formula on $n$ variables, where each clause occurs independently with probability $\alpha/2n$, exhibits a sharp threshold at $\alpha=1$. We provide a simple conceptual proof of this fact based on branching process arguments. We also study a generalized 2-SAT model in which each clause occurs independently but with probability $\alpha_i/2n$ where $i \in {0,1,2 }$ is the number of positive literals in that clause. We use 2-type branching process arguments to determine the satisfiability threshold for this model in terms of the maximum eigenvalue of the branching matrix.