We used near-infrared 2MASS data to construct visual extinction maps of a sample of Southern Bok globules utilizing the NICE method . We derived radial extinction profiles of dense cores identified in the globules and analyzed their stability against gravitational collapse with isothermal Bonnor-Ebert spheres . The frequency distribution of the stability parameter ( \xi _ { max } ) of these cores shows that a large number of them are located in stable states , followed by an abrupt decrease of cores in unstable states . This decrease is steeper for globules with associated IRAS point sources than for starless globules . Moreover , globules in stable states have a Bonnor-Ebert temperature of T = 15 \pm 6 K , while the group of critical plus unstable globules has a different temperature of T = 10 \pm 3 K. Distances were estimated to all the globules studied in this work and the spectral class of the IRAS sources was calculated . No variations were found in the stability parameters of the cores and the spectral class of their associated IRAS sources . On the basis of ^ { 13 } CO J = 1–0 molecular line observations , we identified and modeled a blue-assymetric line profile toward a globule of the sample , obtaining an upper limit infall speed of 0.25 km s ^ { -1 } .