  We demonstrate that in a two component dark matter (DM) set up, when DM$_1$
is equilibrated with the thermal bath, the other DM$_2$, in spite of having
feeble or negligible interaction with the SM particles, can be brought to
equilibrium just by having sizeable interaction with DM$_1$. We propose that
such DM candidates (DM$_2$) should be classified into a category called
pseudo-FIMP (pFIMP) having unique freeze-out characteristics which depend on
the thermal DM partner. The draft elaborates upon the pFIMP properties from a
generic coupled Boltzmann Equations (cBEQ) in a model independent way, followed
by a concrete model illustration.
