In a connection method between speech communication terminals, a first speech communication terminal states a first category including multiple speech codec modes in an SDP offer and transmits to a second communication speech terminal. The second communication speech terminal selects, and states in an SDP answer as a second category, multiple modes from among the first category stated in the SDP offer, and transmits to the first speech communication terminal. At least one of the SDP offer and the SDP answer states a request for a maximum bandwidth or a bandwidth of a mode of highest priority from among the speech codec modes included in the second category.