There is substantial empirical evidence showing that peer effects matter in many activities. The workhorse model in empirical work on peer effects is the linear-in-means (LIM) model, whereby it is assumed that agents are linearly affected by the mean action of their peers. We develop a new general model of peer effects that relaxes the linear assumption of the best-reply functions and the mean peer behavior and that encompasses the spillover, conformist model, and LIM model as special cases. Then, using data on adolescent activities in the U.S., we structurally estimate this model. We find that for many activities, individuals do not behave according to the LIM model. We run some counterfactual policies and show that imposing the mean action as an individual social norm is misleading and leads to incorrect policy implications.