Methane (CH4) on Mars has attracted a great deal of attention since it was first detected in January 2003. As methane is considered a potential marker for past/present biological or geological activity, any possible detection would require evidence with strong statistical significance. Ethane (C2H6) and ethylene (C2H4) are also relevant chemical species as their shorter lifetimes in the Martian atmosphere make them excellent tracers for recent and ongoing releases. If detected, a CH4/C2Hn ratio could aid in constraining the potential source of organic production. Here we present the results of an extensive search for hydrocarbons in the Martian atmosphere in 240,000 solar occultation measurements performed by the ExoMars Trace Gas Orbiter/NOMAD instrument from April 2018 to April 2019. The observations are global, covering all longitudes and latitudes from 85°N to 85°S, and sampled from 6 to 100 km altitude with a typical vertical resolution of 2 km. There were no statistically significant detections of organics and new stringent upper limits for global ethane and ethylene were set at 0.1 ppbv and 0.7 ppbv, respectively. No global background level of methane was observed, obtaining an upper limit of 0.06 ppbv, in agreement with early results from ExoMars (Korablev et al., 2019). Dedicated searches for localized plumes at more than 2000 locations provided no positive detections, implying that if methane were released in strong and rapid events, the process would have to be sporadic.