“ Cometary ” Blue Compact Dwarf Galaxies ( iI , C BCDs ) are characterized by an off–center starburst close to the end of their elongated stellar bodies . This rare phenomenon may carry some clues on how collective star formation ignites and propagates in gas–rich low–mass stellar systems . This off–center burst may be a fortuitous enhancement of the otherwise moderate star–forming activity of a dwarf irregular ( dI ) , or may be caused by a set of special properties of such systems or their environment . We attempt here a first investigation of this issue by analysing two prototypical examples of cometary dwarf galaxies , the nearby iI , C BCDs Markarian 59 and Markarian 71 , both containing an extraordinarily luminous H ii region in the outskirts of a dI–like host . Using deep ground–based spectrophotometric data Obtained at the German–Spanish Astronomical Center , Calar Alto , operated by the Max–Planck–Institute for Astronomy , Heidelberg , jointly with the Spanish National Commission for Astronomy . ^ { , } Obtained at the Kitt Peak National Observatory , National Optical Astronomy Observatories , operated by the Association of Universities for Research in Astronomy , Inc. , under cooperative agreement with the National Science Foundation . and HST images Based on observations with the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute , which is operated by AURA , INC. , under NASA contract No . NAS 5–26555 . , we study the physical state of the starburst regions and the structural properties of the underlying irregular galaxies . We find that the average metallicities show small scatter in the vicinity of the star-forming regions and along the major axis of Mkn 59 which suggests that mixing of heavy elements must have been efficient on scales of several kpc . The azimuthally averaged radial intensity distributions of the underlying host galaxies in either iI , C BCD can be approximated by an exponential law with a central surface brightness and scale length that is intermediate between typical iE/nE BCDs and dwarf irregulars . Spectral population synthesis models in combination with colour magnitude diagrams and colour profiles yield a most probable formation age of \sim 2 Gyr for the low surface brightness ( LSB ) host galaxies in both iI , C BCDs , with upper age limits of \sim 4 Gyr for Mkn 59 and \sim 3 Gyr for Mkn 71 , i.e . significantly lower than the typical age of several Gyr derived for the LSB component of iE/nE BCDs . These findings raise the question whether iI , C systems form a distinct physical class within BCDs with respect to the age and structural properties of their hosts , or whether they represent an evolutionary stage connecting young i0 BCDs and “ classical ” iE/nE BCDs . In spite of the scarcity of available data , a review of the properties of analogous objects studied in the local universe and at medium redshifts provides some support for this evolutionary hypothesis .