Given two sets of points P and Q, a group nearest neighbor (GNN) query retrieves the point(s) of P with the smallest sum of distances to all points in Q. Consider, for instance, three users at locations q₁, q₂ and q₃ that want to find a meeting point (e.g., a restaurant); the corresponding query returns the data point p that minimizes the sum of Euclidean distances |pq_i| for 1≤i ≤3. Assuming that Q fits in memory and P is indexed by an R-tree, we propose several algorithms for finding the group nearest neighbors efficiently. As a second step, we extend our techniques for situations where Q cannot fit in memory, covering both indexed and non-indexed query points. An experimental evaluation identifies the best alternative based on the data and query properties.