Based on more than 10.000 observations of rental flats in Vienna, collected from 2004 to 2006, we apply Bayesian structured additive regression models to estimate hedonic price equations. For this purpose we use explanatory variables such as the buildingís year of construction, its total floor space, the number of rooms, the floor the domicile is located on, the existence of a garage or parking area, the existence of an elevator, balcony or terrace as well as its current condition. Non-linear effects of continuous covariates as well as a smooth time trend are modeled nonparametrically through Bayesian versions of penalized splines. Unobserved district-specific heterogeneity is modeled in two ways: First, discrete correlated spatial effects follow a Markov random field prior with the postal code serving as a location variable. Second, in order to permit spatial variation in the nonlinear price gradients, we introduce multiplicative random effects ( random scaling factors) for nonlinear covariates. This allows highly nonlinear implicit price functions to vary within a regularized framework. Therefore, we account for spatial heterogeneity as well as spatial correlation. Using this model extension, we find substantial spatial variation in house price gradients, leading to a significant improvement of model quality and predictive power.