A low-insertion-force connector assembly comprising: one connector receiving one terminal; and the other connector receiving a mating terminal, the one connector including: a driving lever having a circular-arc-shaped wall part, and a gear part arranged in a circular-arc shape, the driving lever disposed rotatively along an upper wall portion of a housing of the one connector, and pivotally supported onto the upper wall portion, a gear wheel engaging with the gear part; and a gear member having a spiral groove engaged with a driven projection of the other connector, wherein the one connector is provided with a safety circuit unit slidable in an axial direction of the driving lever, wherein the other connector is provided with a small connector for connecting with the safety circuit unit, wherein the safety circuit unit is provided with a case having a side wall and a horizontal ceiling wall, the ceiling wall being formed to have a flange part, a lower face of the flange part is capable of abutting an upper face of the upper wall portion of the one connector housing at a position of sliding lower end, and the flange part is capable of projecting upward further than the driving lever at a position of sliding upper end, wherein at a provisional connector-engaging position in which the driven projection is introduced into the spiral groove, the flange part is positioned on the circular-arc-shaped wall, and therefore the safety circuit unit is prevented from sliding from the position of sliding upper end in a connection direction with the small connector, wherein at a position where the one connector is engaged with the other connector and where the circular-arc-shaped wall is separated from the flange part by rotating the driving lever clockwise, the safety circuit unit is permitted to slide in the connection direction with the small connector to the position of sliding lower end, and wherein at the position of sliding lower end, the safety circuit unit is connected to the small connector, and therefore the flange part abuts onto an end of the circular-arc-shaped wall in a counterclockwise direction, so that the driving lever is prevented from rotating in a counterclockwise direction. one connector receiving one terminal; and the other connector receiving a mating terminal, the one connector including: a driving lever having a circular-arc-shaped wall part, and a gear part arranged in a circular-arc shape, the driving lever disposed rotatively along an upper wall portion of a housing of the one connector, and pivotally supported onto the upper wall portion, a gear wheel engaging with the gear part; and a gear member having a spiral groove engaged with a driven projection of the other connector, wherein a driving lever having a circular-arc-shaped wall part, and a gear part arranged in a circular-arc shape, the driving lever disposed rotatively along an upper wall portion of a housing of the one connector, and pivotally supported onto the upper wall portion, a gear wheel engaging with the gear part; and a gear member having a spiral groove engaged with a driven projection of the other connector, wherein the one connector is provided with a safety circuit unit slidable in an axial direction of the driving lever, wherein the other connector is provided with a small connector for connecting with the safety circuit unit, wherein the safety circuit unit is provided with a case having a side wall and a horizontal ceiling wall, the ceiling wall being formed to have a flange part, a lower face of the flange part is capable of abutting an upper face of the upper wall portion of the one connector housing at a position of sliding lower end, and the flange part is capable of projecting upward further than the driving lever at a position of sliding upper end, wherein at a provisional connector-engaging position in which the driven projection is introduced into the spiral groove, the flange part is positioned on the circular-arc-shaped wall, and therefore the safety circuit unit is prevented from sliding from the position of sliding upper end in a connection direction with the small connector, wherein at a position where the one connector is engaged with the other connector and where the circular-arc-shaped wall is separated from the flange part by rotating the driving lever clockwise, the safety circuit unit is permitted to slide in the connection direction with the small connector to the position of sliding lower end, and wherein at the position of sliding lower end, the safety circuit unit is connected to the small connector, and therefore the flange part abuts onto an end of the circular-arc-shaped wall in a counterclockwise direction, so that the driving lever is prevented from rotating in a counterclockwise direction.