Competition of χ(2P) quarkonia and continuum in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.svg"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:

We discuss the production of DD¯ pairs in e+e− collisions, where D refers to either D0 or D+. The continuum mechanism with the t/u-channel vector-meson D* exchanges are considered. The results of the calculation depend on the parameter of the off-shell form-factor for the virtual D* mesons. The D*Dγ coupling constants are found from the D* → Dγ decays. We find relatively large contribution for the D0D¯0 channel and much smaller contribution in the D+D− channel. In the second case we consider also the D ± exchanges. We conclude that the bump at MD0D¯0=3.8 GeV observed by the Belle and BaBar Collaborations has rather continuum origin than it corresponds to the broad resonance χc0(3860). We discuss also production of the χc2(3930) resonance which is a candidate for the χc2(2P) state. This state can decay into both DD¯ channels, however the branching fractions are not well known at present. From a comparison of our model results to the BaBar data we find B(χc2(3930)→DD¯)=0.58±0.13 using the two-photon width Γγγ=0.544 keV (obtained for the Buchmüller-Tye potential) evaluated within the light-front approach (NRQCD limit). Our finding of Γγγ×B(χc2(3930)→DD¯)=0.32±0.07 keV is close to the Belle and BaBar results. Realistic predictions of the differential distributions in several variables and integrated cross-sections are given for the Belle II kinematics.