We propose a new flexible deep convolutional neural network (convnet) to perform fast neural style transfers. Our network is trained to solve approximately, but rapidly, the artistic style transfer problem of [Gatys et al.] for arbritary styles. While solutions already exist, our network is uniquely flexible by design: it can be manipulated at runtime to enforce new constraints on the final output. As examples, we show that it can be modified to perform tasks such as fast photorealistic style transfer, or fast video style transfer with short term consistency, with no retraining. This flexibility stems from the proposed architecture which is obtained by unrolling the gradient descent algorithm used in [Gatys et al.]. Regularisations added to [Gatys et al.] to solve a new task can be reported on-the-fly in our network, even after training.