A composition for controlling pests comprising a compound represented by the formula or N -oxide thereof and a compound represented by the formula; the formula: wherein A 1 represents -NR 7 -, an oxygen atom, or a sulfur atom; A 2 represents a nitrogen atom or =CR 8 -; R 1 represents a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X; R 2, R 3 and R 4 are the same or different to each other and each independently represent a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X, a -OR 10 group, a -C(OR 10) 3 group, a - S m R 10 group, a -S 2 NR 10 R 11 group, a -NR 10 R 11 group, a - NR 10 CO 2 R 11 group, a -NR 10 C R 11 group, a -CO 2 R 10 group, a - C R 10 group, a -C NR 10 R 11 group, a -SF 5 group, a cyano group, a nitro group, a halogen atom, or a hydrogen atom; R 5 and R 6 are the same or different to each other and each independently represent a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X, a -OR 10 group, a -S m R 10 group, a - S 2 NR 10 R 11 group, a -NR 10 R 11 group, a -NR 10 CO 2 R 11 group, a - NR 10 C R 11 group, a -CO 2 R 10 group, a -C R 10 group, a - C NR 10 R 11 group, -OC R 10, a -SF 5 group, a -SH group, a cyano group, a nitro group, a halogen atom, or a hydrogen atom, except for a case in which R 5 and R 6 are both hydrogen atoms; R 7 represents a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group W, a -CO 2 R 10 group, a -C R 10 group, a -CH 2 CO 2 R 10 group, a C3-C6 cycloalkyl group, or a hydrogen atom; R 8 represents a C1-C6 alkyl group which may be substituted with one or more halogen atoms, a -OR 10 group, a -S m R 10 group, a -NR 10 R 11 group, a -CO 2 R 10 group, a - C R 10 group, a cyano group, a nitro group, a halogen atom, or a hydrogen atom; R 10 and R 11 are the same or different to each other and each independently represent a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X or a hydrogen atom, except for a - S m R 10 group wherein m is 1 or 2 and R 10 is a hydrogen atom; each m independently represents 0, 1 or 2; and n represents 0, 1 or 2; Group X comprising: a C1-C6 alkoxy group which may be substituted with one or more halogen atoms, a C3-C6 cycloalkyl group which may be substituted with one or more halogen atoms or one or more C1-C3 alkyl groups, a cyano group, a hydroxy group, and a halogen atom; Group W comprising: a C1-C6 alkoxy group which may be substituted with one or more halogen atoms, a C3-C6 cycloalkyl group which may be substituted with one or more halogen atoms, a hydroxy group, a halogen atom, and a cyano group; the formula: wherein R 1 represents a hydrogen atom or a methyl group; and R 2 represents a methyl group, a difluoromethyl group, or a trifluoromethyl group. A 1 represents -NR 7 -, an oxygen atom, or a sulfur atom; A 2 represents a nitrogen atom or =CR 8 -; R 1 represents a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X; R 2, R 3 and R 4 are the same or different to each other and each independently represent a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X, a -OR 10 group, a -C(OR 10) 3 group, a - S m R 10 group, a -S 2 NR 10 R 11 group, a -NR 10 R 11 group, a - NR 10 CO 2 R 11 group, a -NR 10 C R 11 group, a -CO 2 R 10 group, a - C R 10 group, a -C NR 10 R 11 group, a -SF 5 group, a cyano group, a nitro group, a halogen atom, or a hydrogen atom; R 5 and R 6 are the same or different to each other and each independently represent a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X, a -OR 10 group, a -S m R 10 group, a - S 2 NR 10 R 11 group, a -NR 10 R 11 group, a -NR 10 CO 2 R 11 group, a - NR 10 C R 11 group, a -CO 2 R 10 group, a -C R 10 group, a - C NR 10 R 11 group, -OC R 10, a -SF 5 group, a -SH group, a cyano group, a nitro group, a halogen atom, or a hydrogen atom, except for a case in which R 5 and R 6 are both hydrogen atoms; R 7 represents a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group W, a -CO 2 R 10 group, a -C R 10 group, a -CH 2 CO 2 R 10 group, a C3-C6 cycloalkyl group, or a hydrogen atom; R 8 represents a C1-C6 alkyl group which may be substituted with one or more halogen atoms, a -OR 10 group, a -S m R 10 group, a -NR 10 R 11 group, a -CO 2 R 10 group, a - C R 10 group, a cyano group, a nitro group, a halogen atom, or a hydrogen atom; R 10 and R 11 are the same or different to each other and each independently represent a C1-C6 alkyl group which may be substituted with one or more atoms or groups selected from Group X or a hydrogen atom, except for a - S m R 10 group wherein m is 1 or 2 and R 10 is a hydrogen atom; each m independently represents 0, 1 or 2; and n represents 0, 1 or 2; a C1-C6 alkoxy group which may be substituted with one or more halogen atoms, a C3-C6 cycloalkyl group which may be substituted with one or more halogen atoms or one or more C1-C3 alkyl groups, a cyano group, a hydroxy group, and a halogen atom; a C1-C6 alkoxy group which may be substituted with one or more halogen atoms, a C3-C6 cycloalkyl group which may be substituted with one or more halogen atoms, a hydroxy group, a halogen atom, and a cyano group; R 1 represents a hydrogen atom or a methyl group; and R 2 represents a methyl group, a difluoromethyl group, or a trifluoromethyl group.