We report detailed investigation of nulling and drifting behavior of two pulsars PSRs J1741-0840 and J1840-0840 observed from the Giant Meterwave Radio Telescope at 625 MHz. PSR J1741-0840 was found to show a nulling fraction (NF) of around 30% +/- 5% while PSR J1840-0840 was shown to have an NF of around 50% +/- 6%. We measured drifting behavior from different profile components in PSR J1840-0840 for the first time with the leading component showing drifting with 13.5 +/- 0.7 periods while the weak trailing component showed drifting of around 18 +/- 1 periods. Large nulling hampers accuracy of these quantities derived using standard Fourier techniques. A more accurate comparison was drawn from driftband slopes, measured after sub-pulse modeling. These measurements revealed interesting sporadic and irregular drifting behavior in both pulsars. We conclude that the previously reported different drifting periodicities in the trailing component of PSR J1741-0840 is likely due to the spread in these driftband slopes. We also find that both components of PSR J1840-0840 show similar driftband slopes within the uncertainties. Unique nulling-drifting interaction is identified in PSR J1840-0840 where, on most occasions, the pulsar tends to start nulling after what appears to be the end of a driftband. Similarly, when the pulsar switches back to an emission phase, on most occasions it starts at the beginning of a new driftband in both components. Such behaviors have not been detected in any other pulsars to our knowledge. We also found that PSR J1741-0840 seems to have no memory of its previous burst phase while PSR J1840-0840 clearly exhibits memory of its previous state even after longer nulls for both components. We discuss possible explanations for these intriguing nulling-drifting interactions seen in both pulsars based on various pulsar nulling models.