Algebra and coalgebra are widely used to model data types in functional programming languages and proof assistants. Their use permits to better structure the computations and also to enhance the expressivity of a language or of a proof system. The use of algebras and coalgebras in proof assistants relies on the possibility of integrating them in strongly normalizing languages such as System F or the calculus of constructions without loosing the good logical properties of the calculus. In fact, in those systems it is possible to define weak (initial) algebras and weak (final) coalgebra by using parametric polymorphism. In this work we study the problem of defining algebras and coalgebra in Light Linear Logic, a system characterizing the complexity class P. Due to the stratified nature of Light Linear Logic, we need to consider stratified versions of (weak) algebras and coalgebras. Thanks to these notions we are able to define standard algebraic and coalgebraic data types in our language.