Basic postures such as sit, stand and lie are ubiquitous in human interaction. In order to build robots that aid and support humans in their daily life, we need to understand how posture categories can be learned and recognized. This paper presents an unsupervised learning approach to posture recognition for a biped humanoid robot. The approach is based on Slow Feature Analysis (SFA), a biologically inspired algorithm for extracting slowly changing signals from signals varying on a fast time scale. Two experiments are carried out: First, we consider the problem of recognizing static postures in a multimodal sensory stream which consists of visual and proprioceptive stimuli. Secondly, we show how to extract a low-dimensional representation of the sensory state space which is suitable for posture recognition in a more complex setting. We point out that the beneficial performance of SFA in this task can be related to the fact that SFA computes manifolds which are used in robotics to model invariants in motion and behavior. Based on this insight, we also propose a method for using SFA components for guided exploration of the state space.