Context :

Aims : Weak G-band ( WGB ) stars are a rare class of cool luminous stars that present a strong depletion in carbon , but also lithium abundance anomalies that have been little explored in the literature since the first discovery of these peculiar objects in the early 50 ’ s .
Here we focus on the Li-rich WGB stars and report on their evolutionary status .
We explore different paths to propose a tentative explanation for the lithium anomaly .

Methods : Using archive data , we derive the fundamental parameters of WGB ( T _ { \mathrm { eff } } , \log g , \log ( L / L _ { \odot } ) ) using Hipparcos parallaxes and recent temperature scales .
From the equivalent widths of Li resonance line at 6707 Å , we uniformly derive the lithium abundances and apply when possible NLTE corrections following the procedure described by Lind et al .
( 2009 ) .
We also compute dedicated stellar evolution models in the mass range 3.0 to 4.5 M _ { \odot } , exploring the effects of rotation-induced and thermohaline mixing .
These models are used to locate the WGB stars in the H-R diagram and to explore the origin of the abundance anomalies .

Results : The location of WGB stars in the H-R diagram shows that these are intermediate mass stars of masses ranging from 3.0 to 4.5 M _ { \odot } located at the clump , which implies a degeneracy of their evolutionary status between subgiant/red giant branch and core helium burning phases .
The atmospheres of a large proportion of WGB stars ( more than 50 % ) exhibit lithium abundances A ( Li ) \geq 1.4 dex similar to Li-rich K giants .
The position of WGB stars along with the Li-rich K giants in the H-R diagram however indicates that both are well separated groups .
The combined and tentatively consistent analysis of the abundance pattern for lithium , carbon and nitrogen of WGB stars seems to indicate that carbon underabundance could be decorrelated from the lithium and nitrogen overabundances .

Conclusions :