Network neutrality has recently attracted a lot of attention but search neutrality is also becoming a vivid subject of discussion because a non-neutral search may prevent some relevant content from being accessed by users. We propose in this paper to model two situations of a non-neutral search engine behavior, which can rank the link propositions according to the pro t a search can generate for it instead of just relevance: the case when the search engine owns some content, and the case when it imposes a tax on organic links, a bit similarly to what it does for commercial links. We analyze the particular (and deterministic) situation of a single keyword, and describe the problem for the whole potential set of keywords.