The relationship between environmental degradation and economic growth has become a prominent topic in recent decades, increasing multidisciplinary approaches across a wide range of studies. Analyzing the economy-environment nexus is significant because most countries attempt to limit environmental deterioration while pursuing economic growth. This paper studies the non-linear cross-correlations between economic growth and environmental degradation on a sample of five developed European countries - France, Germany, Spain, Norway, and the United Kingdom. The study is performed using two approaches: multifractal detrended cross-correlation analysis and wavelet-based analysis. According to the empirical tests, there are non-linear cross-correlations between economic growth and environmental degradation in all five countries. For each country, multifractal metrics such as Hurst exponents, scaling exponents, and multifractal spectra are computed to show the significance of all time-series pairs. The strongest multifractal features have been observed in France, Norway, and Spain. Shuffling the series suggests that multifractality in the cross-correlations arises both from a broad probability density function and from different long-term correlations. Wavelets are applied to detrend all data sets before computing the cross-correlation. Moreover, the wavelet coherence is computed as a measure for analyzing interdependencies across time and frequencies. Except for France and Spain, Wavelet-detrended cross-correlation values are considerably lower than cross-correlation values of the raw data sets, which indicates that the interdependence between growth and environmental degradation is rather long-term. In terms of wavelet coherence, results vary among the countries, with France and Spain showing the highest and most persistent coherence values. [ABSTRACT FROM AUTHOR]