In most industrialized countries a stagnation of urban mobility and of car traffic is observed since the early 2000s. In France, the Report on traffic by the Traffic Accounts Committee Transport of the Nation shows a similar trend breakdown confirmed the Household Travel Surveys in most large cities, namely Lille, Lyon, Strasbourg, and also by the National Transportation and Travel Survey which shows that this apparent new trend can be attributed mainly to the inhabitants of large urban centers and permits a global overview of mobility: the trips are less frequent (continuous day) and less exclusively by car (multi-modal behavior of young adults), the car ownership decreases in the center of the Paris Region as also in the Centre of London. Does this leveling off of traffic translate a saturation phenomenon (decoupling growth in traffic and revenue in the densest regions or beyond a certain standard of living ?) or rather the superposition of opposing trends (continued growth in rural and suburban areas vs. decline among residents of the densest areas) ? Is it a structural phenomenon (ageing population ...) or cyclical due to the increase and volatility in fuel prices, recession...? We will examine these issues in light of data collected in France, completed by additional data of developed countries, to search an answer to these questions and also compare them with case studies on a few Mexican cities to see if these trends could also be present in emergent economies and on what horizon ?