This paper studies 2-layer RAC drawings of bipartite graphs. The contribution is as follows: (
) We prove that the problem of computing the maximum 2-layer RAC subgraph is NP-hard even when the vertex ordering on one layer is fixed; this extends a previous NP-hardness result that allows the vertices to be permuted on each layer. (
) We describe a 3-approximation algorithm for the maximum 2-layer RAC subgraph problem when the vertex ordering on each layer is not fixed, and a heuristic for the case that the vertex ordering on one of the layers is fixed. (
) We present an experimental study that evaluates the effectiveness of the proposed approaches.