[en] On the basis of sub-arcsecond imaging obtained at the ESO NTT with SUSI and the ESO ADONIS adaptive optics system at the 3.6m telescope, we resolve and study the core components of the LMC OB association LH 39. The central star of the association, the rare transition object R 84, is also investigated using CASPEC echelle spectroscopy at the ESO 3.6m telescope. A new, powerful image restoration code that conserves the fluxes allows us to obtain the magnitudes and colors of the components. We bring out some 30 stars in a ~16"x16" area centered on R 84. At a resolution of 0.19"(FWHM), the closest components to R 84 are shown to be stars #21 and #7 lying at 1.1"NW and 1.7"NW respectively of the transition star. The former is possibly a blue star of V=16.7mag and the latter with its V=17.5mag is the reddest star of the field, after R 84. Star #7 turns out to be too faint to correspond to the red M2 supergiant previously reported to contaminate the spectrum of R 84. If the late-type spectrum is due to a line-of-sight supergiant with a luminosity comparable to R 84, it should lie closer than 0.12" to R 84. The transition star shows spectral variability between 1982 and 1991. We also note some slight radial velocity variations of the Of emission lines over timescales of several years. Furthermore, we derive the spectral types of two of the brightest stars of the cluster, using long slit spectra obtained at the NTT telescope equipped with EMMI, and discuss the apparent absence of O type stars in this association.