We describe searches for decays to two-body charmless final states η ′ η , η ′ π 0 and η π 0 of B 0 mesons produced in e + e − annihilation. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 232 × 10 6 produced B ¯¯¯ B pairs. The results for branching fractions are, in units of 10 − 6 (upper limits at 90% C.L.): B ( B 0 → η ′ η ) = 0.2 + 0.7 − 0.5 ± 0.4 ( < 1.7 ) , B ( B 0 → η π 0 ) = 0.6 + 0.5 − 0.4 ± 0.1 ( < 1.3 ) , and B ( B 0 → η ′ π 0 ) = 0.8 + 0.8 − 0.6 ± 0.1 ( < 2.1 ) . The first error quoted is statistical and the second systematic.