The study of processes involving flavour-changing neutral currents provides a particularly promising probe for New Physics beyond the Standard Model of particle physics. These processes are forbidden at tree level and proceed through loop processes, which are strongly suppressed in the Standard Model. Cross-sections for these processes can be significantly enhanced by contributions from new particles as they are proposed in most extentions of the Standard Model. This thesis presents searches for two flavour-changing neutral current decays, B± ! K±μ+μ− and B0 d ! K¤μ+μ−. The analysis was performed on 4.1 fb−1 of data collected by the DØ detector in Run II of the Fermilab Tevatron. Candidate events for the decay B± ! K±μ+μ− were selected using a multi-variate analysis technique and the number of signal events determined by a fit to the invariant mass spectrum. Normalising to the known branching fraction for B± ! J/ÃK±, a branching fraction of B(B± ! K± μ+μ−) = 6.45 ± 2.24 (stat) ± 1.19 (syst) × 10−7 (1) was measured. The branching fraction for the decay B0 d ! K¤μ+μ− was determined in a similar way. Normalizing to the known branching fraction for B0 d ! J/ÃK¤, a branching fraction of B(B0 d ! K¤ μ+μ−) = 11.15 ± 3.05 (stat) ± 1.94 (syst) × 10−7 (2) was measured. All measurements are in agreement with the Standard Model.