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We study the chemistry of small hydrocarbons in the photon-dominated regions(PDRs) associated with the ultra-compact HII region Mon R2. Our goal is todetermine the variations of the abundance of small hydrocarbons in a high-UVirradiated PDR and investigate their chemistry. We present an observationalstudy of CH, CCH and c-C$_3$H$_2$ in Mon R2 combining data obtained with theIRAM 30m telescope and Herschel. We determine the column densities of thesespecies, and compare their spatial distributions with that of polycyclicaromatic hydrocarbon (PAH). We compare the observational results with differentchemical models to explore the relative importance of gas-phase, grain-surfaceand time-dependent chemistry in these environments. The emission of the smallhydrocarbons show different patterns. The CCH emission is extended while CH andc-C$_3$H$_2$ are concentrated towards the more illuminated layers of the PDR.The ratio of the column densities of c-C$_3$H$_2$ and CCH shows spatialvariations up to a factor of a few, increasing from$N(c-C$_3$H$_2$)/N(CCH)\approx0.004$ in the envelope to a maximum of$\sim0.015-0.029$ towards the 8$\mu$m emission peak. Comparing these resultswith other galactic PDRs, we find that the abundance of CCH is quite constantover a wide range of G$_0$, whereas the abundance of c-C$_3$H$_2$ is higher inlow-UV PDRs. In Mon R2, the gas-phase steady-state chemistry can accountrelatively well for the abundances of CH and CCH in the most exposed layers ofthe PDR, but falls short by a factor of 10 to reproduce c-C$_3$H$_2$.  In the molecular envelope, time-dependent effects and grain surface chemistryplay a dominant role in determining the hydrocarbons abundances. Our studyshows that CCH and c-C$_3$H$_2$ present a complex chemistry in which UVphotons, grain-surface chemistry and time dependent effects contribute todetermine their abundances.

Spatial distribution of small hydrocarbons in the neighborhood of the Ultra Compact HII region Monoceros R2