We investigate the contribution of star formation to the growth of stellar mass in galaxies over the redshift range 0.5 < z < 1.1 by studying the redshift evolution of the specific star formation rate ( SSFR ) , defined as the star formation rate per unit stellar mass . We use an I -band selected sample of 6180 field galaxies from the Munich Near-Infrared Cluster Survey ( MUNICS ) with spectroscopically calibrated photometric redshifts . The SSFR decreases with stellar mass at all redshifts . The low SSFRs of massive galaxies indicates that star formation does not significantly change their stellar mass over this redshift range : The majority of massive galaxies have assembled the bulk of their mass before redshift unity . Furthermore , these highest mass galaxies contain the oldest stellar populations at all redshifts . The line of maximum SSFR runs parallel to lines of constant star formation rate . With increasing redshift , the maximum SFR is generally increasing for all stellar masses , from \mathrm { SFR } \simeq 5 \ > M _ { \odot } \ > \mathrm { yr } ^ { -1 } at z \simeq 0.5 to \mathrm { SFR } \simeq 10 \ > M _ { \odot } \ > \mathrm { yr } ^ { -1 } at z \simeq 1.1 . We also show that the large SSFRs of low-mass galaxies can not be sustained over extended periods of time . Finally , our results do not require a substantial contribution of merging to the growth of stellar mass in massive galaxies over the redshift range probed . We note that highly obscured galaxies which remain undetected in our sample do not affect these findings for the bulk of the field galaxy population .