<p>In this study, slant helices are investigated via quasi-frame (abbv. q-frame) in four-dimensional Euclidean space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb{E}}^{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">E</mi> </mrow> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation>. The notion of <i>k</i>-type slant q-helices is introduced in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathbb{E}}^{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">E</mi> </mrow> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation>. Each of the q-frame fields <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\left\{ {{\mathbf{T}},{\mathbf{N}}_{q} ,{\mathbf{B}}_{q} ,{\mathbf{C}}_{q} } \right\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="}" open="{"> <mrow> <mi mathvariant="bold">T</mi> <mo>,</mo> <msub> <mi mathvariant="bold">N</mi> <mi>q</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="bold">B</mi> <mi>q</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="bold">C</mi> <mi>q</mi> </msub> </mrow> </mfenced> </math></EquationSource> </InlineEquation> which makes constant angles with a non-zero fixed axis is surveyed one by one. Also, the conditions for each type of q-helices are obtained and their associations to each other are analyzed in detail.</p>