Communication between two neighboring nodes is the most basic operation in wireless networks. Yet very little research has focused on the local delay, defined as the mean time it takes a node to connect to a nearby neighbor. This problem is non-trivial when link distances are random but static, as is the case when the node distribution of a static network is modeled as a stochastic point process. We first consider the interference-free case, where links are independent, to study how fading and power control affect the delay in links of random distance. We find that power control is essential to keep the delay finite, and that randomized power control can drastically reduce the required (mean) power for finite local delay. Secondly, we study the local delay in a Poisson network with ALOHA, including both interference and noise. In this case we present an analytical bound on the local delay.