The Emotional Intelligence (EI) concept is widely discussed and many authors are questioning the exiting relations between emotional intelligence and general intelligence understood as a general factor. With the aim of give an answer to the question we will proceed to analyse the existing relation between itself, the general intelligence and the different intelligences proposed by Gardner, with the aim of delimiting or not the different theory conceptions.For that we have used a questionnaire for evaluating the emotional intelligence designed by Ruben Dario Chiriboga and Jenny Elisabeth Franco is made of 60 items with four answer's options (never, something, almost always, and always) and includes the following abilities: self-conscious, self control, emotional profitability, empathy and social ability.The sample is composed by 98 students (from 7 until 8 years old) belonging to three different schools of the provinces of Murcia and Alicante (Spain).The results show that psychometric characteristic of the EI scale referred to reliability is adequate, as it shows the internal consistency coefficient a by Cronbach offering a value of .7409.The correlations between the different abilities that define EI and the general intellectual quotient are very low and non significant, what confirms the studies done by Mayer and Salovey (1997).We can also observe that the correlations between the different EI scale components are unequal. On one side, we find that the self-knowledge and social abilities variables are the ones that they have less relation with the rest of abilities, been the emotional use and empathy variables the ones that show more relation. So, the ability for been in a stage of permanent search and persistency in the execution of the aims facing always the problems and finding solutions that will define the emotional use variable, as well as, the ability to understand the needs feelings and problems of other people, be in the own skin of the others and responding correctly to the emotional reactions of the variable empathy, that will be the ones defining the construct of the emotional intelligence.In the other side, the relation between the EI and the multiple intelligences by Gardner is very low (with the exception of the existing relation between the emotional use variable and the logical mathematical intelligence). The Pearson's correlation indexes between the EI scale measures variables and the total marks of the multiple intelligences evaluation scales are very low.This result confirms the idea that the intelligence is multifunctional and there are several intelligences independent one from each others (Stemberg 1985; Gardner 1983, 1999b).The IE is a constructor that still requires research and deepening, and according to the results of some researches done in the same subject show its importance within the study of social and intellectual human competence.