An exercise machine suitable for exercising a person's muscles contains a frame (100Y or 100Z), a seat (102) situated over the frame, a seatback (104 or 104Y), a connection mechanism (106 or 106Y) for flexibly and adjustably connecting the seatback to the frame or/and the seat, a pedaling mechanism (112Y or 112Z) connectable to the frame and having a pair of movable foot pedals (140), and a pair of frame legs (302 or 470). The seatback is typically capable of swiveling and can be segmented to facilitate swiveling. The legs can typically be retracted for enabling the machine to be used for stationary cycling when the legs are retracted and as an elevated exercise bench when the legs extend downward. Alternatively, the legs may permanently elevate the frame, seat, and seatback above the underlying surface. With the legs extending downward and with the pedaling mechanism connected to the frame, the pedaling mechanism can typically be tilted downward to facilitate use of the machine as an exercise bench. The machine may include mechanisms for rapidly switching the legs between their retracted and extended positions and for rapidly switching the seatback between inclined and flat positions.