Recurrent neural networks (NN) with long short-term memory (LSTM) are the current state of the art to model long term dependencies. However, recent studies indicate that NN language models (LM) need only limited length of history to achieve excellent performance. In this paper, we extend the previous investigation on LSTM network based n-gram modeling to the domain of automatic speech recognition (ASR). First, applying recent optimization techniques and up to 6-layer LSTM networks, we improve LM perplexities by nearly 50% relative compared to classic count models on three different domains. Then, we demonstrate by experimental results that perplexities improve significantly only up to 40-grams when limiting the LM history. Nevertheless, the ASR performance saturates already around 20-grams despite across sentence modeling. Analysis indicates that the performance gain of LSTM NNLM over count models results only partially from the longer context and cross sentence modeling capabilities. Using equal context, we show that deep 4-gram LSTM can significantly outperform large interpolated count models by performing the backing off and smoothing significantly better. This observation also underlines the decreasing importance to combine state-of-the-art deep NNLM with count based model.