A bobbin carrying apparatus in a fine spinning machine which is provided with first and second transporting devices (T1,T2), a connection portion for connecting the first and second transporting devices, first and second solenoid valves (32,33), and a control device (C) is disclosed. Each of the first and second transporting devices is provided with a peg tray path (16), a transporting member which can reciprocate so that peg trays are moved, and air cylinders for reciprocating the transporting members. The control device (C) controls the first and second solenoid valves (32,33) so that the point in time when the first air cylinder (21) starts operating is delayed relative to the point in time when the second air cylinder (22) starts operating.; The bobbin carrying apparatus is provided with first and second operating period sensing portions (S1a,S1b,S2a,S2b) for sensing the operating periods of the first and second air cylinders (21,22), respectively. The control device (C) corrects the difference in time when the first and second air cylinders (21,22) start operating in accordance with the fluctuation in the operating period as sensed by the two operating period sensing portionsso that peg trays on the first transporting device (T1) do not apply a pressing force to peg trays on the second transporting device (T2).