Atmospheric organic vapors play essential roles in the formation of secondary organic aerosol. Source identification of these vapors is thus fundamental to understanding their emission sources and chemical evolution in the atmosphere and their further impact on air quality and climate change. In this study, a Vocus proton-transfer-reaction time-of-flight mass spectrometer (PTR-TOF) was deployed in two forested environments, the Landes forest in southern France and the boreal forest in southern Finland, to measure atmospheric organic vapors, including both volatile organic compounds (VOCs) and their oxidation products. For the first time, we performed binned positive matrix factorization (binPMF) analysis on the complex mass spectra acquired with the Vocus PTR-TOF and identified various emission sources as well as oxidation processes in the atmosphere. Based on separate analysis of low- and high-mass ranges, 15 PMF factors in the Landes forest and nine PMF factors in the Finnish boreal forest were resolved, showing a high similarity between the two sites. Particularly, terpenes and various terpene reaction products were separated into individual PMF factors with varying oxidation degrees, such as lightly oxidized compounds from both monoterpene and sesquiterpene oxidation, monoterpene-derived organic nitrates, and monoterpene more oxidized compounds. Factors representing monoterpenes dominated the biogenic VOCs in both forests, with lower contributions from the isoprene factors and sesquiterpene factors. Factors of the lightly oxidized products, more oxidized products, and organic nitrates of monoterpenes/sesquiterpenes accounted for 8 %-12 % of the measured gas-phase organic vapors in the two forests. Based on the interpretation of the results relating to oxidation processes, further insights were gained regarding monoterpene and sesquiterpene reactions. For example, a strong relative humidity (RH) dependence was found for the behavior of sesquiterpene lightly oxidized compounds. High concentrations of these compounds only occur at high RH; yet similar behavior was not observed for monoterpene oxidation products.