An exercise machine suitable for exercising a person's muscles contains a frame (100), a seat (102) situated over the frame, a seatback (104), a connection mechanism (106) for flexibly and adjustably connecting the seatback to the frame or/and the seat, and a pedaling mechanism (112) connectable to the frame. The pedaling mechanism has a pair of movable pedals (140) that revolve generally around a pedaling axis. The seatback is capable of swiveling.