Using data from the United States spanning the period between 1970 and 2017, we analyze the economic assimilation of subsequent arrival cohorts of Mexican and Central American immigrants, the more economically disadvantaged group of immigrants. We compare their wage and employment probability to that of similarly aged and educated natives across various cohorts of entry. We find that all cohorts started with a disadvantage of 40-45 percent relative to the average US native, and eliminated about half of it in the 20 years after entry. They also started with no employment probability disadvantage at arrival and they overtook natives in employment rates so that they were 5-10 percent more likely to be employed 20 years after arrival. We also find that recent cohorts, arriving after 1995, did better than earlier cohorts both in initial gap and convergence. We show that Mexicans and Central Americans working in the construction sector and in urban areas did better in terms of gap and convergence than others. Finally, also for other immigrant groups, such as Chinese and Indians, recent cohorts did better than previous ones.