Multiple block coded modulations (MBCM) are studied. One characteristic of the studied MBCM schemes is that they have both a block and a trellis structure. A general rule for deriving branch variables so as to establish a decoding trellis is presented. Examples of MBCM schemes employing 8-PSK and 16-PSK constellations are given. Two different methods using these schemes are proposed for producing unequal error protection. Computer simulations are done to show the UEP ability.