Non-equilibrium models, chemical models, gas-phase models and cloud interface models were used to reproduce the abundances of all observed species in the Zeta Per and HD 27778 interstellar clouds. Non-equilibrium models reproduce all observed abundances (except CH+). Chemical models reproduce the observed abundances of NH and CN. Gas-phase models and cloud interface models fail to explain the observed high abundance of CN. The observation of NH in Zeta Per and HD 27778 provides proof for the presence of grain surface reactions leading to molecules other than H2. Predictions are made that NH2 and NH3 should have abundances not much below that of NH if NH3 instead of NH is formed on grains.