Chemically peculiar red giants, Li-rich K giants and Weak G-band (WGB) stars, are rare class of cool luminous stars whose spctra show strong Li resonance line at 6707 Ang and very weak or absent G-bands of the CH~A$^{2}Delta$ - X$^{2}Pi$ system at 4300 AA.
Some of these stars are also associated with other peculiarities like: Infrared excess, rapid rotation, activity, and binarity.
The origin of such anomalies in these class of stars are not well understood.
To understand the underlying physical process for such anomalies, and to check the relation between their peculiarities,
we have initiated a systematic study of Li-rich K giants and WGB stars.
In this talk, I will discuss the properties of Li-rich K giants and WGB stars, and the results obtained from various observations.