This thesis describes the analyses of the rare charmless hadronic B meson decays B[sup 0] [yields] [phi]K[sup 0] and B[sup 0] [yields] K*[sup +][pi][sup -], using 20.58 fb[sup -1] of e[sup +]e[sup -] data taken at the [Upsilon](4S) resonance. The data were taken with the BABAR detector during its first run at the PEP-II asymmetric e[sup +]e[sup -] collider. Measurements of these modes using a counting technique are presented with the branching fractions [Beta](B[sup 0] [yields] [phi]K[sup 0]) = (9.3 [+-] 3.4(stat.) [+-] 1.1(syst.)) x 10[sup -6] with a significance of 4.9[sigma], and [Beta](B[sup 0] [yields] K*[sup +][pi][sup -]) = (20.8 [+-] 9.3(stat.) [+-] 2.1(syst.)) x 10[sup -6] with a significance of 3.0[sigma]. For the latter, an upper limit of [Beta](B[sup 0] [yields] K*[sup +][pi][sup -])

An upper limit has been extracted, at the 90% C.L, for the rare charmless hadronic B meson decay B ± → a0(980)±[pi]0, where a0(980)± →[eta][pi]± and [eta]→[gamma][gamma] or [eta]→ [pi]+[pi]-[pi]0. The analysis was based on a sample of approximately 340.7 fb-1 of data taken at the (4S) resonance with the BABAR detector at the PEP-II e+e- collider at SLAC from May 1999 to August 2006. The sample contains (379.9 ± 4.2) million B$\bar{B}$ pairs.

An upper limit has been extracted, at the 90% C.L, for the rare charmless hadronic B meson decay B ± → a0(980)±?0, where a0(980)± →??± and ?????????? or ???????? ?+?-?0. The analysis was based on a sample of approximately 340.7 fb-1 of data taken at the (4S) resonance with the BABAR detector at the PEP-II e+e- collider at SLAC from May 1999 to August 2006. The sample contains (379.9 ± 4.2) million B$ar{B}$ pairs.