Whittle-Matern class of covariance functions and the several families constructed by applying the classical properties have been largely utilized in the applications; however, a serious drawback of the above families concerns they are always non negative, hence they are not able to model structures characterized by negative correlation. Indeed, in many applications, the phenomenon under study can be characterized by negative correlation, hence covariance models with negative values are needed. Although some theoretical results regarding families of covariance functions characterized by negative correlation have been given in the literature, however the general problem about the requirements such that a covariance function can be obtained through the difference between two covariance functions has been faced only recently in the complex and, as a special case, in the real domain. Moreover, with respect to the traditional covariance models, the new families of covariance functions are more flexible since by properly choosing the parameters values, the same models can be adopted for both covariance functions which are always positive and covariances which are negative in a subset of the corresponding domain. Some examples illustrating the presence of negative correlation have been provided.