“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 data1,2 and HST images3, 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 ∼ 2 Gyr for the low surface brightness (LSB) host galaxies in both iI,C BCDs, with upper age limits of ∼ 4 Gyr for Mkn 59 and ∼ 3 Gyr for Mkn 71, i.e. significantly lower than the typical age Send offprint requests to: K.G. Noeske (firstname.lastname@example.org) 1 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. 2 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. 3 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. 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.