We present new broad-band optical and near-infrared CCD imaging together with deep optical intermediate-resolution spectroscopy of Mkn 1087 and its surrounding objects. We analyze the morphology and colors of the stellar populations of the brightest objects, some of them star-formation areas, as well as the kinematics, physical conditions and chemical composition of the ionized gas associated with them. Mkn 1087 does not host an Active Galactic Nucleus, but it could be a Luminous Compact Blue Galaxy. Although it was classified as a suspected Wolf-Rayet galaxy, we do not detect the spectral features of these sort of massive stars. Mkn 1087 shows morphological and kinematical features that can be explained assuming that it is in interaction with two nearby galaxies: the bright KPG 103a and a dwarf (MB˜-18) star-forming companion. We argue that this dwarf companion is not a tidal object but an external galaxy because of its low metallicity [12+log(O/H) = 8.24] with respect to the one derived for Mkn 1087 [12+log(O/H) = 8.57] and its kinematics. Some of the non-stellar objects surrounding Mkn 1087 are connected by bridges of matter with the main body, host star-formation events and show similar abundances despite their different angular distances. These facts, together their kinematics, suggest that they are tidal dwarf galaxies formed from material stripped from Mkn 1087. A bright star-forming region at the south of Mkn 1087 (knot #7) does not show indications of being a tidal galaxy or the product of a merging process as suggested in previous works. We argue that Mkn 1087 and its surroundings should be considered a group of galaxies. Based on observations made with several telescopes operated on the islands of La Palma and Tenerife by the Isaac Newton Group of Telescopes and Instituto de Astrofísica de Canarias in the Spanish Observatories of Roque de Los Muchachos and Teide of the Instituto de Astrofísica de Canarias.